Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22623065 | C2 | semidirect |
| 2. #22620377 | C2 | semidirect |
| 3. #22611658 | C2 | semidirect |
| 4. #22608011 | C2 | semidirect |
| 5. C73×#1975 | C2 | semidirect |
| 47. C2×#11924003 | D4 | semidirect |
| 51. C2×Q16×C73 | D4 | semidirect |
| 53. C2×D8×C73 | D4 | semidirect |
| 167. #1975 | D73 | semidirect |
| 169. C73 | #13340 | semidirect |
| 199. C2×Q16 | D292 | semidirect |
| 205. C2×D8 | D292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623065 | 2 |
| #22620377 | 2 |
| #22611658 | 2 |
| #22608011 | 2 |
| C73×#1975 | 2 |
| #13340 | 73 |