Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
114 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 114 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 |
|---|---|---|
| 1. C2×#10596942 | C2 | semidirect |
| 4. #11924469 | C2 | semidirect |
| 5. #11924460 | C2 | semidirect |
| 6. #11924459 | C2 | semidirect |
| 38. C22×C37 | Q16 | semidirect |
| 52. C37 | #467 | semidirect |
| 90. C22 | #10596942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10596942 | 2 |
| C22×#64436 | 2 |
| #11924515 | 2 |
| #11924469 | 2 |
| #11924460 | 2 |
| #11924459 | 2 |
| C22⋊Q8×C37 | 2 |
| #467 | 37 |