Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
606 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 606 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 17. C2×#14556525 | C4 | semidirect |
| 18. C2×#14556522 | C4 | semidirect |
| 19. C2×#107×C73 | C4 | semidirect |
| 174. C73 | #11364 | semidirect |
| 183. C2×#107 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625631 | 2 |
| #22625617 | 2 |
| #22625610 | 2 |
| #22625596 | 2 |
| C2×#17988624 | 2 |
| #11364 | 73 |