Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
270 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 111 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. #27131329 | C2 | semidirect |
| 3. #27131320 | C2 | semidirect |
| 4. #27131314 | C2 | semidirect |
| 5. #27131307 | C2 | semidirect |
| 6. #27131290 | C2 | semidirect |
| 7. C22×Q8×C379 | C2 | semidirect |
| 52. C379 | #536 | semidirect |
| 55. C22×Q8 | D379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20258606 | 2 |
| #27131329 | 2 |
| #27131320 | 2 |
| #27131314 | 2 |
| #27131307 | 2 |
| #27131290 | 2 |
| C22×Q8×C379 | 2 |
| #536 | 379 |