Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
134 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 134 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×#10596939 | C2 | semidirect |
| 2. C22×#64436 | C2 | semidirect |
| 3. #11924510 | C2 | semidirect |
| 4. #11924469 | C2 | semidirect |
| 5. #11924457 | C2 | semidirect |
| 6. #11924456 | C2 | semidirect |
| 7. #121×C37 | C2 | semidirect |
| 37. #64436 | D4 | semidirect |
| 43. C22×C37 | D8 | semidirect |
| 60. C37 | #466 | semidirect |
| 64. #121 | D37 | semidirect |
| 106. C22 | #10596939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10596939 | 2 |
| C22×#64436 | 2 |
| #11924510 | 2 |
| #11924469 | 2 |
| #11924457 | 2 |
| #11924456 | 2 |
| #121×C37 | 2 |
| #466 | 37 |