Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
122 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 122 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. Q8×Dic379 | C2 | semidirect |
| 4. #27131262 | C2 | semidirect |
| 6. C8×Dic379 | C2 | semidirect |
| 7. #103×C379 | C2 | semidirect |
| 10. #20258593 | C4 | semidirect |
| 27. C379⋊C8 | C2×C4 | semidirect |
| 29. Q8×C379 | C2×C4 | semidirect |
| 44. Dic379 | SD16 | semidirect |
| 49. C379 | C4×SD16 | semidirect |
| 55. #103 | D379 | semidirect |
| 72. Q8 | C4×D379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20258593 | 2 |
| Q8×Dic379 | 2 |
| #27131293 | 2 |
| #27131262 | 2 |
| #27131253 | 2 |
| C8×Dic379 | 2 |
| #103×C379 | 2 |
| C4×SD16 | 379 |