Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
730 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22609625 | C2 | semidirect |
| 2. #22607757 | C2 | semidirect |
| 3. #22607752 | C2 | semidirect |
| 55. C2×Q8×C73 | M16 | semidirect |
| 62. C2×D4×C73 | M16 | semidirect |
| 170. C73 | #7631 | semidirect |
| 217. C2×Q8 | #11924012 | semidirect |
| 224. C2×D4 | #11924012 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22609625 | 2 |
| #22607757 | 2 |
| #22607752 | 2 |
| C73×#2297 | 2 |
| #7631 | 73 |