Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
1056 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 169 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 | C23×#381 | C2 |
| hypercenter | #381 | D23 |
| hypocenter | C23 | #2404 |
| LCS | G ▷ C23×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#67288 | C2 | semidirect |
| 2. C2×#10625053 | C2 | semidirect |
| 3. C22×(C2×D23)⋊C4 | C2 | semidirect |
| 4. #13092330 | C2 | semidirect |
| 5. #13092327 | C2 | semidirect |
| 6. #13092295 | C2 | semidirect |
| 7. #13092294 | C2 | semidirect |
| 8. C23×#381 | C2 | semidirect |
| 16. C22×D92 | C22 | semidirect |
| 17. C22×C4×D23 | C22 | semidirect |
| 18. C22×Dic46 | C22 | semidirect |
| 24. C2×(C2×D23)⋊C4 | C22 | semidirect |
| 26. C23×#95 | C22 | semidirect |
| 27. C23×#95 | C22 | semidirect |
| 28. C23⋊#95 | C22 | semidirect |
| 37. C22×C4×C23 | D4 | semidirect |
| 43. C2×C22⋊D23 | D4 | semidirect |
| 82. C22×D23 | #41 | semidirect |
| 134. #381 | D23 | semidirect |
| 160. #95 | C2×D23 | semidirect |
| 161. #95 | C2×D23 | semidirect |
| 162. C23 | #2404 | semidirect |
| 189. C22×C4 | D92 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67288 | 2 |
| C2×#10625053 | 2 |
| C22×(C2×D23)⋊C4 | 2 |
| #13092330 | 2 |
| #13092327 | 2 |
| #13092295 | 2 |
| #13092294 | 2 |
| C23×#381 | 2 |
| #2404 | 23 |