Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 162 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×#20258606 | C2 | semidirect |
| 2. C2×#20258595 | C2 | semidirect |
| 3. C2×D3032 | C2 | semidirect |
| 4. #27131305 | C2 | semidirect |
| 5. #27131256 | C2 | semidirect |
| 6. #27131253 | C2 | semidirect |
| 7. C22⋊C8×C379 | C2 | semidirect |
| 26. Dic758 | D4 | semidirect |
| 30. D1516 | D4 | semidirect |
| 64. C379 | #449 | semidirect |
| 72. C22⋊C8 | D379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20258606 | 2 |
| C2×#20258595 | 2 |
| C2×D3032 | 2 |
| #27131305 | 2 |
| #27131256 | 2 |
| #27131253 | 2 |
| C22⋊C8×C379 | 2 |
| #449 | 379 |