Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
216 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 95 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. #27131326 | C2 | semidirect |
| 3. #27131320 | C2 | semidirect |
| 4. #27131317 | C2 | semidirect |
| 5. #27131313 | C2 | semidirect |
| 6. #27131311 | C2 | semidirect |
| 8. Q8×Dic379 | C2 | semidirect |
| 9. #27131293 | C2 | semidirect |
| 10. #27131290 | C2 | semidirect |
| 11. C22⋊Q8×C379 | C2 | semidirect |
| 73. C379 | #542 | semidirect |
| 81. C22⋊Q8 | D379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27131330 | 2 |
| #27131326 | 2 |
| #27131320 | 2 |
| #27131317 | 2 |
| #27131313 | 2 |
| #27131311 | 2 |
| #27131305 | 2 |
| Q8×Dic379 | 2 |
| #27131293 | 2 |
| #27131290 | 2 |
| C22⋊Q8×C379 | 2 |
| #542 | 379 |