Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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×#10596962 | C2 | semidirect |
| 2. #11924569 | C2 | semidirect |
| 3. #11924564 | C2 | semidirect |
| 4. #11924558 | C2 | semidirect |
| 5. C2×M16×C37 | C2 | semidirect |
| 11. #10596962 | C22 | semidirect |
| 12. C2×D148 | C22 | semidirect |
| 14. C2×Dic74 | C22 | semidirect |
| 15. M16×C37 | C22 | semidirect |
| 16. C2×C8×C37 | C22 | semidirect |
| 17. Dic148 | C22 | semidirect |
| 18. D296 | C22 | semidirect |
| 19. #10596930 | C22 | semidirect |
| 50. C37 | #575 | semidirect |
| 55. C2×M16 | D37 | semidirect |
| 68. M16 | C2×D37 | semidirect |
| 69. C2×C8 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10596962 | 2 |
| #11924569 | 2 |
| #11924564 | 2 |
| #11924558 | 2 |
| C2×M16×C37 | 2 |
| #575 | 37 |