Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
106 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 40 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. #11924624 | C2 | semidirect |
| 2. #11924623 | C2 | semidirect |
| 3. #11924606 | C2 | semidirect |
| 4. #11924601 | C2 | semidirect |
| 5. #11924600 | C2 | semidirect |
| 6. C8×#3866 | C2 | semidirect |
| 18. SD16×C37 | C4 | semidirect |
| 19. #10596942 | C4 | semidirect |
| 20. #10596939 | C4 | semidirect |
| 21. #10596930 | C4 | semidirect |
| 52. C37 | #443 | semidirect |
| 64. SD16 | #3866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11924624 | 2 |
| #11924623 | 2 |
| #11924606 | 2 |
| #11924601 | 2 |
| #11924600 | 2 |
| C8×#3866 | 2 |
| #11924557 | 2 |
| #443 | 37 |