Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D92 |
| commutator, cosocle | C2×C4×C23 | C24 |
| Frattini | C2×C4 | C23×D23 |
| Fitting | C23×#443 | C2 |
| socle | C2×C23 | D42 |
| hypercenter | #443 | D23 |
| hypocenter | C23 | #3290 |
| LCS | G ▷ C2×C4×C23 ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #443 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13093231 | C2 | semidirect |
| 2. #13093229 | C2 | semidirect |
| 3. #13093219 | C2 | semidirect |
| 4. #13092801 | C2 | semidirect |
| 5. #13092693 | C2 | semidirect |
| 6. #13092688 | C2 | semidirect |
| 7. #13092680 | C2 | semidirect |
| 8. #13092596 | C2 | semidirect |
| 9. #13092591 | C2 | semidirect |
| 10. #13092535 | C2 | semidirect |
| 11. C23×#443 | C2 | semidirect |
| 12. #10625161 | C22 | semidirect |
| 15. C23×#131 | C22 | semidirect |
| 16. #10625122 | C22 | semidirect |
| 27. #10625079 | C22 | semidirect |
| 28. C2×Dic92 | C22 | semidirect |
| 33. C2×#67263 | C22 | semidirect |
| 35. #10625072 | C22 | semidirect |
| 36. #10625046 | C22 | semidirect |
| 37. C23×#108 | C22 | semidirect |
| 38. C23×#104 | C22 | semidirect |
| 39. C4×C8×C23 | C22 | semidirect |
| 40. #10625006 | C22 | semidirect |
| 41. #10625005 | C22 | semidirect |
| 42. #10625001 | C22 | semidirect |
| 44. #10624987 | C22 | semidirect |
| 154. #443 | D23 | semidirect |
| 184. #131 | C2×D23 | semidirect |
| 187. #108 | C2×D23 | semidirect |
| 190. #104 | C2×D23 | semidirect |
| 193. C4×C8 | C2×D23 | semidirect |
| 194. C23 | #3290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13093231 | 2 |
| #13093229 | 2 |
| #13093219 | 2 |
| #13092801 | 2 |
| #13092693 | 2 |
| #13092688 | 2 |
| #13092680 | 2 |
| #13092596 | 2 |
| #13092591 | 2 |
| #13092535 | 2 |
| C23×#443 | 2 |
| #3290 | 23 |