Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
696 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 234 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. #22626030 | C2 | semidirect |
| 3. #22625985 | C2 | semidirect |
| 5. #22625863 | C2 | semidirect |
| 6. #22625858 | C2 | semidirect |
| 36. #14556585 | C8 | semidirect |
| 64. #11924007 | C2×C8 | semidirect |
| 75. C42×C73 | C2×C8 | semidirect |
| 126. C73 | #23375 | semidirect |
| 194. C42 | #11924036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626030 | 2 |
| #22626003 | 2 |
| #22625985 | 2 |
| #22625876 | 2 |
| #22625863 | 2 |
| #22625858 | 2 |
| #22612479 | 2 |
| #23375 | 73 |