Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #27131326 | C2 | semidirect |
| 2. #27131322 | C2 | semidirect |
| 3. #27131320 | C2 | semidirect |
| 4. #27131316 | C2 | semidirect |
| 5. #27131307 | C2 | semidirect |
| 7. C4×D1516 | C2 | semidirect |
| 8. C4×D1516 | C2 | semidirect |
| 9. #27131288 | C2 | semidirect |
| 10. C42×D379 | C2 | semidirect |
| 11. C4×Q8×C379 | C2 | semidirect |
| 74. C379 | #529 | semidirect |
| 82. C4×Q8 | D379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27131326 | 2 |
| #27131322 | 2 |
| #27131320 | 2 |
| #27131316 | 2 |
| #27131307 | 2 |
| #27131306 | 2 |
| C4×D1516 | 2 |
| #27131288 | 2 |
| C42×D379 | 2 |
| C4×Q8×C379 | 2 |
| #529 | 379 |