Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
3464 conjugacy classes of subgroups; only the 365 normal subgroups are shown.
This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 365 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×#379 | C2 |
| socle, cosocle | C23×C23 | C24 |
| prime radical | C25×D23 | C2 |
| hypercenter | #379 | D23 |
| hypocenter | C23 | C2×#379 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C22⋊C4×D23 | C2 | semidirect |
| 3. #13092273 | C2 | semidirect |
| 4. #13092272 | C2 | semidirect |
| 5. C23×#379 | C2 | semidirect |
| 8. C24×D23 | C4 | semidirect |
| 11. C22×C4×D23 | C22 | semidirect |
| 12. C2×C22⋊C4×C23 | C22 | semidirect |
| 13. C2×C22⋊Dic23 | C22 | semidirect |
| 14. C2×(C2×D23)⋊C4 | C22 | semidirect |
| 17. C24×C23 | C2×C4 | semidirect |
| 25. C23×D23 | C2×C4 | semidirect |
| 29. C22×C4×C23 | C23 | semidirect |
| 30. C22×Dic23 | C23 | semidirect |
| 48. C22×D23 | C22⋊C4 | semidirect |
| 60. C22×C23 | C2×C22⋊C4 | semidirect |
| 68. C2×D23 | C2×C22⋊C4 | semidirect |
| 76. #379 | D23 | direct (N × H) |
| 81. D23 | #379 | direct (N × H) |
| 91. C2×C22⋊C4 | C2×D23 | semidirect |
| 92. C23 | C2×#379 | semidirect |
| 104. C24 | C4×D23 | semidirect |
| 108. C22×C4 | C22×D23 | semidirect |
| 143. C22 | C22⋊C4×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×D23 | 2 |
| C2×C22⋊C4×D23 | 2 |
| #13092273 | 2 |
| #13092272 | 2 |
| C23×#379 | 2 |
| C2×#379 | 23 |