Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
234 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 62 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. #22625580 | C2 | semidirect |
| 2. #22625527 | C2 | semidirect |
| 3. #22624956 | C2 | semidirect |
| 4. #22624890 | C2 | semidirect |
| 5. #22624889 | C2 | semidirect |
| 6. #22624850 | C2 | semidirect |
| 64. D8×C73 | M16 | semidirect |
| 116. C73 | #12078 | semidirect |
| 160. D8 | #11924038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625580 | 2 |
| #22625527 | 2 |
| #22624956 | 2 |
| #22624890 | 2 |
| #22624889 | 2 |
| #22624850 | 2 |
| #22611804 | 2 |
| #12078 | 73 |