Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #11924584 | C2 | semidirect |
| 2. #11924568 | C2 | semidirect |
| 3. #11924567 | C2 | semidirect |
| 4. #11924559 | C2 | semidirect |
| 5. #11924558 | C2 | semidirect |
| 6. Q16×D37 | C2 | semidirect |
| 7. #11924542 | C2 | semidirect |
| 8. C2×Q16×C37 | C2 | semidirect |
| 60. C37 | #578 | semidirect |
| 67. C2×Q16 | D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11924584 | 2 |
| #11924568 | 2 |
| #11924567 | 2 |
| #11924559 | 2 |
| #11924558 | 2 |
| Q16×D37 | 2 |
| #11924542 | 2 |
| C2×Q16×C37 | 2 |
| #578 | 37 |