Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
246 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 70 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. #22625529 | C2 | semidirect |
| 2. #22625527 | C2 | semidirect |
| 3. #22624957 | C2 | semidirect |
| 4. #22624890 | C2 | semidirect |
| 5. #22624889 | C2 | semidirect |
| 6. #22624848 | C2 | semidirect |
| 35. #14556532 | C8 | semidirect |
| 55. D584 | C2×C8 | semidirect |
| 61. #11924003 | C2×C8 | semidirect |
| 64. D8×C73 | C2×C8 | semidirect |
| 116. C73 | #12067 | semidirect |
| 160. D8 | #11924036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625529 | 2 |
| #22625527 | 2 |
| #22624957 | 2 |
| #22624890 | 2 |
| #22624889 | 2 |
| #22624848 | 2 |
| #22611804 | 2 |
| #12067 | 73 |