Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 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. #27131325 | C2 | semidirect |
| 2. #27131323 | C2 | semidirect |
| 3. #27131319 | C2 | semidirect |
| 4. #27131314 | C2 | semidirect |
| 5. #27131310 | C2 | semidirect |
| 7. C4×Dic758 | C2 | semidirect |
| 8. C4×D1516 | C2 | semidirect |
| 9. C4×C22⋊D379 | C2 | semidirect |
| 10. #27131288 | C2 | semidirect |
| 11. C2×C42×C379 | C2 | semidirect |
| 74. C379 | #529 | semidirect |
| 86. C2×C42 | D379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27131325 | 2 |
| #27131323 | 2 |
| #27131319 | 2 |
| #27131314 | 2 |
| #27131310 | 2 |
| #27131305 | 2 |
| C4×Dic758 | 2 |
| C4×D1516 | 2 |
| C4×C22⋊D379 | 2 |
| #27131288 | 2 |
| C2×C42×C379 | 2 |
| #529 | 379 |