Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
1056 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 185 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, socle, cosocle | C23×C23 | C24 |
| Fitting | C22×#41×C23 | C2 |
| hypercenter | C22×#41 | D23 |
| hypocenter | C23 | #2404 |
| LCS | G ▷ C23×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10625108 | C2 | semidirect |
| 2. C22×(C2×D23)⋊C4 | C2 | semidirect |
| 3. #13092328 | C2 | semidirect |
| 4. #13092325 | C2 | semidirect |
| 5. #13092297 | C2 | semidirect |
| 6. #13092296 | C2 | semidirect |
| 7. #13092280 | C2 | semidirect |
| 8. C22×#41×C23 | C2 | semidirect |
| 12. C22×Q8×C23 | C22 | semidirect |
| 14. C22×D4×C23 | C22 | semidirect |
| 16. C23×C4×C23 | C22 | semidirect |
| 20. C2×C22⋊Dic23 | C22 | semidirect |
| 26. C23⋊#95 | C22 | semidirect |
| 27. C23⋊#95 | C22 | semidirect |
| 28. C23⋊#95 | C22 | semidirect |
| 43. C2×D4×C23 | D4 | semidirect |
| 48. C22×C4×C23 | D4 | semidirect |
| 82. C22×D23 | #41 | semidirect |
| 127. C22×#41 | D23 | semidirect |
| 145. C22×Q8 | C2×D23 | semidirect |
| 148. C22×D4 | C2×D23 | semidirect |
| 151. C23×C4 | C2×D23 | semidirect |
| 162. C23 | #2404 | semidirect |
| 180. C2×D4 | C22⋊D23 | semidirect |
| 189. C22×C4 | C22⋊D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625108 | 2 |
| C22×(C2×D23)⋊C4 | 2 |
| #13092328 | 2 |
| #13092325 | 2 |
| #13092297 | 2 |
| #13092296 | 2 |
| #13092280 | 2 |
| C22×#41×C23 | 2 |
| #2404 | 23 |