Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
612 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D23 |
| commutator | C22×C23 | C23×C4 |
| Fitting | C23×#376 | C2 |
| socle, cosocle | C23×C23 | C24 |
| prime radical | C22×D92 | C22 |
| hypercenter | #376 | D23 |
| hypocenter | C23 | #2326 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ #376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×Dic46 | C2 | semidirect |
| 4. #13092323 | C2 | semidirect |
| 6. #13092309 | C2 | semidirect |
| 7. #13092291 | C2 | semidirect |
| 8. #13092287 | C2 | semidirect |
| 9. C23×#376 | C2 | semidirect |
| 24. #10625046 | C4 | semidirect |
| 46. C2×Dic46 | C2×C4 | semidirect |
| 48. C42×C23 | C2×C4 | semidirect |
| 52. (C2×D23)⋊C4 | C2×C4 | semidirect |
| 114. #376 | D23 | semidirect |
| 141. C23 | #2326 | semidirect |
| 168. C42 | C4×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625046 | 2 |
| C2×C4×Dic46 | 2 |
| C2×C4×D92 | 2 |
| #13092323 | 2 |
| #13092319 | 2 |
| #13092309 | 2 |
| #13092291 | 2 |
| #13092287 | 2 |
| C23×#376 | 2 |
| #2326 | 23 |