Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
140 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 41 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. C2×D3032 | C2 | semidirect |
| 2. C2×#20258591 | C2 | semidirect |
| 3. #27131327 | C2 | semidirect |
| 4. #27131293 | C2 | semidirect |
| 5. Dic379⋊C8 | C2 | semidirect |
| 6. #27131251 | C2 | semidirect |
| 7. #102×C379 | C2 | semidirect |
| 26. D1516 | D4 | semidirect |
| 53. Dic379 | D8 | semidirect |
| 60. C379 | #459 | semidirect |
| 68. #102 | D379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3032 | 2 |
| C2×#20258591 | 2 |
| #27131327 | 2 |
| #27131293 | 2 |
| Dic379⋊C8 | 2 |
| #27131251 | 2 |
| #102×C379 | 2 |
| #459 | 379 |