Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
1056 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 173 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×C22⋊C4×C23 | C2 |
| hypercenter | C22×C22⋊C4 | D23 |
| hypocenter | C23 | #2404 |
| LCS | G ▷ C23×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ C22×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#67288 | C2 | semidirect |
| 2. C2×#10625124 | C2 | semidirect |
| 3. #13092329 | C2 | semidirect |
| 4. #13092326 | C2 | semidirect |
| 5. #13092296 | C2 | semidirect |
| 6. #13092293 | C2 | semidirect |
| 7. #13092280 | C2 | semidirect |
| 8. C22×C22⋊C4×C23 | C2 | semidirect |
| 16. C22×D92 | C22 | semidirect |
| 17. C22×C4×D23 | C22 | semidirect |
| 18. C22×Dic46 | C22 | semidirect |
| 25. C2×(C2×D23)⋊C4 | C22 | semidirect |
| 26. C23⋊#95 | C22 | semidirect |
| 27. C23⋊#95 | C22 | semidirect |
| 28. C23⋊#95 | C22 | semidirect |
| 39. C22×C4×C23 | D4 | semidirect |
| 48. C2×C22⋊D23 | D4 | semidirect |
| 76. C23×C23 | #41 | semidirect |
| 129. C22×C22⋊C4 | D23 | semidirect |
| 162. C23 | #2404 | semidirect |
| 189. C22×C4 | C22⋊D23 | semidirect |
| 213. C23 | #67288 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67288 | 2 |
| C2×#10625124 | 2 |
| #13092329 | 2 |
| #13092326 | 2 |
| #13092296 | 2 |
| #13092293 | 2 |
| #13092280 | 2 |
| C22×C22⋊C4×C23 | 2 |
| #2404 | 23 |