Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 104 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 |
|---|---|---|
| 1. #27131361 | C2 | semidirect |
| 2. C2×#20258594 | C2 | semidirect |
| 3. #27131338 | C2 | semidirect |
| 4. #27131266 | C2 | semidirect |
| 5. #27131249 | C2 | semidirect |
| 6. #27131248 | C2 | semidirect |
| 51. C379 | #471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27131361 | 2 |
| C2×#20258594 | 2 |
| #27131338 | 2 |
| #27131266 | 2 |
| #27131249 | 2 |
| #27131248 | 2 |
| AGL(1,ℤ/8)×C379 | 2 |
| #471 | 379 |