Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D421 |
| commutator, socle, cosocle | C22×C421 | C24 |
| Fitting | C2×C22⋊C4×C421 | C2 |
| hypercenter | C2×C22⋊C4 | D421 |
| hypocenter | C421 | #538 |
| LCS | G ▷ C22×C421 ▷ C421 | |
| UCS | C1 ◁ C22 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27212359 | C2 | semidirect |
| 2. #27212352 | C2 | semidirect |
| 3. #27212348 | C2 | semidirect |
| 4. #27212345 | C2 | semidirect |
| 5. #27212340 | C2 | semidirect |
| 6. #27212339 | C2 | semidirect |
| 7. #27212335 | C2 | semidirect |
| 8. C4×C22⋊D421 | C2 | semidirect |
| 9. C2×C22⋊C4×C421 | C2 | semidirect |
| 10. C2×Dic842 | C22 | semidirect |
| 11. C2×D1684 | C22 | semidirect |
| 15. C2×C4×D421 | C22 | semidirect |
| 16. C4⋊Dic421 | C22 | semidirect |
| 17. C4⋊Dic421 | C22 | semidirect |
| 18. #20269750 | C22 | semidirect |
| 19. #20269750 | C22 | semidirect |
| 23. #20269748 | C22 | semidirect |
| 24. #20269748 | C22 | semidirect |
| 25. C4×Dic421 | C22 | semidirect |
| 74. C421 | #538 | semidirect |
| 84. C2×C22⋊C4 | D421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27212359 | 2 |
| #27212352 | 2 |
| #27212348 | 2 |
| #27212345 | 2 |
| #27212340 | 2 |
| #27212339 | 2 |
| #27212335 | 2 |
| C4×C22⋊D421 | 2 |
| C2×C22⋊C4×C421 | 2 |
| #538 | 421 |