Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27131379 | C2 | semidirect |
| 2. #27131378 | C2 | semidirect |
| 3. #27131364 | C2 | semidirect |
| 4. #27131363 | C2 | semidirect |
| 5. #27131360 | C2 | semidirect |
| 6. #27131352 | C2 | semidirect |
| 7. #27131351 | C2 | semidirect |
| 8. C2×#20258596 | C2 | semidirect |
| 9. Q16×D379 | C2 | semidirect |
| 10. #27131339 | C2 | semidirect |
| 11. #137×C379 | C2 | semidirect |
| 87. C379 | #578 | semidirect |
| 94. #137 | D379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27131379 | 2 |
| #27131378 | 2 |
| #27131364 | 2 |
| #27131363 | 2 |
| #27131360 | 2 |
| #27131352 | 2 |
| #27131351 | 2 |
| C2×#20258596 | 2 |
| Q16×D379 | 2 |
| #27131339 | 2 |
| #137×C379 | 2 |
| #578 | 379 |