Finite Group DatabasebetaFinite Group DatabasebetaOrder 24256.
106 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 45 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. #27131339 | C2 | semidirect |
| 3. #27131338 | C2 | semidirect |
| 4. #27131266 | C2 | semidirect |
| 5. #27131259 | C2 | semidirect |
| 6. C4×C379⋊C8 | C2 | semidirect |
| 7. #104×C379 | C2 | semidirect |
| 9. #20258596 | C4 | semidirect |
| 10. #20258594 | C4 | semidirect |
| 11. #20258593 | C4 | semidirect |
| 12. #20258591 | C4 | semidirect |
| 51. C379 | #443 | semidirect |
| 58. #104 | D379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27131351 | 2 |
| #27131339 | 2 |
| #27131338 | 2 |
| #27131266 | 2 |
| #27131259 | 2 |
| C4×C379⋊C8 | 2 |
| #104×C379 | 2 |
| #443 | 379 |