Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
222 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 109 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. #27131330 | C2 | semidirect |
| 2. #27131329 | C2 | semidirect |
| 3. #27131321 | C2 | semidirect |
| 7. C4×Dic758 | C2 | semidirect |
| 8. C4×Dic758 | C2 | semidirect |
| 11. C4×Q8×C379 | C2 | semidirect |
| 45. C4×D379 | Q8 | semidirect |
| 70. C379 | #533 | semidirect |
| 80. C4×Q8 | D379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27131330 | 2 |
| #27131329 | 2 |
| #27131321 | 2 |
| #27131311 | 2 |
| #27131309 | 2 |
| #27131307 | 2 |
| C4×Dic758 | 2 |
| #27131288 | 2 |
| C42×D379 | 2 |
| C4×Q8×C379 | 2 |
| #533 | 379 |