Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
124 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 43 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. C2×#20258596 | C2 | semidirect |
| 4. #27131329 | C2 | semidirect |
| 6. #27131241 | C2 | semidirect |
| 7. C2×Q16×C379 | C2 | semidirect |
| 49. C379 | #497 | semidirect |
| 52. C2×Q16 | D379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20258596 | 2 |
| C2×#20258595 | 2 |
| C2×#20258593 | 2 |
| #27131329 | 2 |
| #27131320 | 2 |
| #27131241 | 2 |
| C2×Q16×C379 | 2 |
| #497 | 379 |