Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
394 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 88 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. #22626291 | C2 | semidirect |
| 2. C4×#14556660 | C2 | semidirect |
| 3. #22624918 | C2 | semidirect |
| 12. #17988964 | C4 | semidirect |
| 17. #17988669 | C4 | semidirect |
| 19. #500×C73 | C4 | semidirect |
| 135. C73 | #11742 | semidirect |
| 137. #500 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626291 | 2 |
| C4×#14556660 | 2 |
| #22624918 | 2 |
| #22620511 | 2 |
| #11742 | 73 |