Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 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. #27131296 | C2 | semidirect |
| 4. #27131264 | C2 | semidirect |
| 5. #27131256 | C2 | semidirect |
| 6. #27131241 | C2 | semidirect |
| 10. #20258594 | C4 | semidirect |
| 21. Dic758 | C2×C4 | semidirect |
| 27. C379⋊C8 | C2×C4 | semidirect |
| 49. C379 | #440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20258594 | 2 |
| #27131296 | 2 |
| D4×Dic379 | 2 |
| #27131264 | 2 |
| #27131256 | 2 |
| #27131241 | 2 |
| #102×C379 | 2 |
| #440 | 379 |