Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
1116 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 197 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, prime radical | C23×D4×C23 | C2 |
| hypercenter | C23×D4 | D23 |
| hypocenter | C23 | #2405 |
| LCS | G ▷ C23×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10625106 | C2 | semidirect |
| 2. C22×C22⋊Dic23 | C2 | semidirect |
| 3. #13092331 | C2 | semidirect |
| 4. #13092297 | C2 | semidirect |
| 5. #13092290 | C2 | semidirect |
| 6. #13092273 | C2 | semidirect |
| 7. #13092273 | C2 | semidirect |
| 16. C23×Dic23 | C22 | semidirect |
| 17. C23×Dic23 | C22 | semidirect |
| 21. C2×C22⋊Dic23 | C22 | semidirect |
| 22. C2×C22⋊Dic23 | C22 | semidirect |
| 23. C2×C22⋊Dic23 | C22 | semidirect |
| 24. C2×C22⋊Dic23 | C22 | semidirect |
| 25. C2×C22⋊Dic23 | C22 | semidirect |
| 27. C2×Dic23⋊C4 | C22 | semidirect |
| 28. C23⋊#95 | C22 | semidirect |
| 126. C22×C23 | #123 | semidirect |
| 171. C23 | #2405 | semidirect |
| 267. C22 | #10625106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625106 | 2 |
| C22×C22⋊Dic23 | 2 |
| #13092331 | 2 |
| #13092297 | 2 |
| #13092290 | 2 |
| #13092273 | 2 |
| C23×D4×C23 | 2 |
| #2405 | 23 |