Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
132 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 51 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. C4×D1516 | C2 | semidirect |
| 3. #27131262 | C2 | semidirect |
| 4. #27131252 | C2 | semidirect |
| 5. #27131251 | C2 | semidirect |
| 6. #27131242 | C2 | semidirect |
| 7. C4×D4×C379 | C2 | semidirect |
| 10. #20258591 | C4 | semidirect |
| 22. D1516 | C2×C4 | semidirect |
| 26. C379⋊C8 | C2×C4 | semidirect |
| 29. D4×C379 | C2×C4 | semidirect |
| 53. C379 | #442 | semidirect |
| 57. C4×D4 | D379 | semidirect |
| 79. D4 | C4×D379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20258591 | 2 |
| C4×D1516 | 2 |
| #27131262 | 2 |
| #27131252 | 2 |
| #27131251 | 2 |
| #27131242 | 2 |
| C4×D4×C379 | 2 |
| #442 | 379 |