Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
508 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 117 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. C22×C16×D73 | C2 | semidirect |
| 3. C2×#17988395 | C2 | semidirect |
| 4. C2×#17988393 | C2 | semidirect |
| 5. #22609966 | C2 | semidirect |
| 6. #22608026 | C2 | semidirect |
| 7. C73×#1382 | C2 | semidirect |
| 51. C2×#11924003 | D4 | semidirect |
| 63. C2×C16×C73 | D4 | semidirect |
| 166. C2×D73 | #359 | semidirect |
| 187. #1382 | D73 | semidirect |
| 188. C73 | #13063 | semidirect |
| 239. C2×C16 | D292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C16×D73 | 2 |
| #22619513 | 2 |
| C2×#17988395 | 2 |
| C2×#17988393 | 2 |
| #22609966 | 2 |
| #22608026 | 2 |
| C73×#1382 | 2 |
| #13063 | 73 |