Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
732 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 2. #22610921 | C2 | semidirect |
| 3. #22608668 | C2 | semidirect |
| 4. #22608525 | C2 | semidirect |
| 7. C73×#1966 | C2 | semidirect |
| 186. D292 | #101 | semidirect |
| 199. Dic146 | #101 | semidirect |
| 234. #1966 | D73 | semidirect |
| 239. C73 | #8473 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623747 | 2 |
| #22610921 | 2 |
| #22608668 | 2 |
| #22608525 | 2 |
| #22608371 | 2 |
| #22608368 | 2 |
| C73×#1966 | 2 |
| #8473 | 73 |