Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
106 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 37 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 |
|---|---|---|
| 2. #27131289 | C2 | semidirect |
| 3. #27131264 | C2 | semidirect |
| 4. #27131253 | C2 | semidirect |
| 5. #27131251 | C2 | semidirect |
| 6. (C2×D379)⋊C8 | C2 | semidirect |
| 7. #106×C379 | C2 | semidirect |
| 51. C379 | #482 | semidirect |
| 56. #106 | D379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27131306 | 2 |
| #27131289 | 2 |
| #27131264 | 2 |
| #27131253 | 2 |
| #27131251 | 2 |
| (C2×D379)⋊C8 | 2 |
| #106×C379 | 2 |
| #482 | 379 |