Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
672 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 189 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×#380 | C2 |
| socle, cosocle | C23×C23 | C24 |
| prime radical | C24×D23 | C22 |
| hypercenter | #380 | D23 |
| hypocenter | C23 | #2312 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #13092309 | C2 | semidirect |
| 3. #13092307 | C2 | semidirect |
| 4. #13092277 | C2 | semidirect |
| 6. C22⋊C4×Dic23 | C2 | semidirect |
| 7. C23×#380 | C2 | semidirect |
| 11. C2×C4⋊C4×C23 | C22 | semidirect |
| 14. C2×(C2×D23)⋊C4 | C4 | semidirect |
| 19. C2×C4⋊Dic23 | C22 | semidirect |
| 20. C2×C4×Dic23 | C22 | semidirect |
| 21. C23×#95 | C22 | semidirect |
| 22. C23⋊#95 | C22 | semidirect |
| 23. C23⋊#95 | C22 | semidirect |
| 105. #380 | D23 | semidirect |
| 119. C2×C4⋊C4 | C2×D23 | semidirect |
| 130. #95 | C2×D23 | semidirect |
| 131. C23 | #2312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×(C2×D23)⋊C4 | 2 |
| #13092309 | 2 |
| #13092307 | 2 |
| #13092277 | 2 |
| #13092272 | 2 |
| C22⋊C4×Dic23 | 2 |
| C23×#380 | 2 |
| #2312 | 23 |