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. #27131324 | C2 | semidirect |
| 3. #27131321 | C2 | semidirect |
| 4. #27131317 | C2 | semidirect |
| 5. #27131315 | C2 | semidirect |
| 6. #27131312 | C2 | semidirect |
| 7. #27131308 | C2 | semidirect |
| 9. C4×Dic758 | C2 | semidirect |
| 10. C4×C22⋊D379 | C2 | semidirect |
| 11. C4×C22⋊D379 | C2 | semidirect |
| 12. #27131290 | C2 | semidirect |
| 13. #27131288 | C2 | semidirect |
| 14. C2×C4×Dic379 | C2 | semidirect |
| 15. C4×D4×C379 | C2 | semidirect |
| 103. C379 | #529 | semidirect |
| 116. C4×D4 | D379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27131326 | 2 |
| #27131324 | 2 |
| #27131321 | 2 |
| #27131317 | 2 |
| #27131315 | 2 |
| #27131312 | 2 |
| #27131308 | 2 |
| #27131303 | 2 |
| C4×Dic758 | 2 |
| C4×C22⋊D379 | 2 |
| #27131290 | 2 |
| #27131288 | 2 |
| C2×C4×Dic379 | 2 |
| C4×D4×C379 | 2 |
| #529 | 379 |