Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1262 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1262 conjugacy classes of subgroups — too many to draw. Only its 191 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. #22623702 | C2 | semidirect |
| 2. #22620849 | C2 | semidirect |
| 3. #22608865 | C2 | semidirect |
| 4. #22608425 | C2 | semidirect |
| 5. #22608255 | C2 | semidirect |
| 6. C73×#2548 | C2 | semidirect |
| 102. C2×Q8×C73 | D8 | semidirect |
| 199. #2548 | D73 | semidirect |
| 203. C73 | #18401 | semidirect |
| 283. C2×Q8 | #11924013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623702 | 2 |
| #22620849 | 2 |
| #22608865 | 2 |
| #22608425 | 2 |
| #22608255 | 2 |
| C73×#2548 | 2 |
| #18401 | 73 |