Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #11924531 | C2 | semidirect |
| 2. #11924527 | C2 | semidirect |
| 3. #11924525 | C2 | semidirect |
| 4. #11924521 | C2 | semidirect |
| 5. #11924512 | C2 | semidirect |
| 7. C4×D148 | C2 | semidirect |
| 8. C4×D148 | C2 | semidirect |
| 9. #11924493 | C2 | semidirect |
| 10. C42×D37 | C2 | semidirect |
| 11. C4×Q8×C37 | C2 | semidirect |
| 75. C37 | #529 | semidirect |
| 82. C4×Q8 | D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11924531 | 2 |
| #11924527 | 2 |
| #11924525 | 2 |
| #11924521 | 2 |
| #11924512 | 2 |
| #11924511 | 2 |
| C4×D148 | 2 |
| #11924493 | 2 |
| C42×D37 | 2 |
| C4×Q8×C37 | 2 |
| #529 | 37 |