Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
122 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 2. C4×Dic758 | C2 | semidirect |
| 4. #27131263 | C2 | semidirect |
| 5. #27131256 | C2 | semidirect |
| 7. C4×C8×C379 | C2 | semidirect |
| 11. #20258595 | C4 | direct (N × H) |
| 22. Dic758 | C2×C4 | semidirect |
| 33. C8×C379 | C2×C4 | semidirect |
| 39. C4×C379 | SD16 | semidirect |
| 49. C379 | C4×SD16 | semidirect |
| 57. C4×C8 | D379 | semidirect |
| 83. C8 | C4×D379 | semidirect |
| 92. C4 | #20258595 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20258595 | 2 |
| C4×Dic758 | 2 |
| C4×D1516 | 2 |
| #27131263 | 2 |
| #27131256 | 2 |
| #27131253 | 2 |
| C4×C8×C379 | 2 |
| C4×SD16 | 379 |