Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
500 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10625090 | C2 | semidirect |
| 2. C2×M16×D23 | C2 | semidirect |
| 3. #13092930 | C2 | semidirect |
| 4. #13092672 | C2 | semidirect |
| 5. #13092671 | C2 | semidirect |
| 6. #13092670 | C2 | semidirect |
| 7. #13092666 | C2 | semidirect |
| 8. #13092665 | C2 | semidirect |
| 9. #13092452 | C2 | semidirect |
| 10. #13092412 | C2 | semidirect |
| 11. C23×#470 | C2 | semidirect |
| 14. C2×Q16×C23 | C22 | semidirect |
| 18. C2×#67274 | C22 | semidirect |
| 23. C2×D184 | C22 | semidirect |
| 34. C23×#106 | C22 | semidirect |
| 35. C23×#103 | C22 | semidirect |
| 36. #10625017 | C22 | semidirect |
| 37. #10625003 | C22 | semidirect |
| 38. #10624999 | C22 | semidirect |
| 39. #10624991 | C22 | semidirect |
| 40. #10624989 | C22 | semidirect |
| 80. C8×D23 | D4 | semidirect |
| 139. #470 | D23 | semidirect |
| 155. C2×Q16 | C2×D23 | semidirect |
| 176. #106 | C2×D23 | semidirect |
| 178. #103 | C2×D23 | semidirect |
| 181. C23 | #3054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625090 | 2 |
| C2×M16×D23 | 2 |
| #13092930 | 2 |
| #13092672 | 2 |
| #13092671 | 2 |
| #13092670 | 2 |
| #13092666 | 2 |
| #13092665 | 2 |
| #13092452 | 2 |
| #13092412 | 2 |
| C23×#470 | 2 |
| #3054 | 23 |