Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
120 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 120 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×#20258595 | C2 | semidirect |
| 2. #27131310 | C2 | semidirect |
| 4. #27131265 | C2 | semidirect |
| 5. #27131256 | C2 | semidirect |
| 6. #27131253 | C2 | semidirect |
| 7. C2×M16×C379 | C2 | semidirect |
| 36. C8×C379 | D4 | semidirect |
| 55. C379 | #468 | semidirect |
| 58. C2×M16 | D379 | semidirect |
| 92. C8 | C22⋊D379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20258595 | 2 |
| #27131310 | 2 |
| #27131305 | 2 |
| #27131265 | 2 |
| #27131256 | 2 |
| #27131253 | 2 |
| C2×M16×C379 | 2 |
| #468 | 379 |