Finite Group DatabasebetaFinite Group DatabasebetaOrder 24896.
334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 103 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×D389 |
| commutator, socle, cosocle | C22×C389 | C24 |
| Fitting | #127×C389 | C2 |
| hypercenter | #127 | D389 |
| hypocenter | C389 | #535 |
| LCS | G ▷ C22×C389 ▷ C389 | |
| UCS | C1 ◁ C22 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#20261965 | C2 | semidirect |
| 2. C2×D4×D389 | C2 | semidirect |
| 3. #27159380 | C2 | semidirect |
| 4. #27159372 | C2 | semidirect |
| 5. #27159371 | C2 | semidirect |
| 6. #27159356 | C2 | semidirect |
| 7. #27159352 | C2 | semidirect |
| 8. #27159341 | C2 | semidirect |
| 9. #127×C389 | C2 | semidirect |
| 12. C2×Dic778 | C22 | semidirect |
| 16. C2×C22⋊D389 | C22 | semidirect |
| 18. C22×Dic389 | C22 | semidirect |
| 20. #20261945 | C22 | semidirect |
| 21. C22⋊Dic389 | C22 | semidirect |
| 23. #20261943 | C22 | semidirect |
| 24. C4×Dic389 | C22 | semidirect |
| 26. C2×D4×C389 | C22 | semidirect |
| 27. C2×D4×C389 | C22 | semidirect |
| 28. C42×C389 | C22 | semidirect |
| 42. C4×D389 | D4 | semidirect |
| 71. C389 | #535 | semidirect |
| 76. #127 | D389 | semidirect |
| 91. C2×D4 | C2×D389 | semidirect |
| 92. C2×D4 | C2×D389 | semidirect |
| 100. C42 | C2×D389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20261965 | 2 |
| C2×D4×D389 | 2 |
| #27159380 | 2 |
| #27159372 | 2 |
| #27159371 | 2 |
| #27159356 | 2 |
| #27159352 | 2 |
| #27159341 | 2 |
| #127×C389 | 2 |
| #535 | 389 |