Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
494 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22618808 | C2 | semidirect |
| 3. C2×#17988393 | C2 | semidirect |
| 4. C2×#17988388 | C2 | semidirect |
| 5. #22608041 | C2 | semidirect |
| 6. #22608020 | C2 | semidirect |
| 7. C73×#1978 | C2 | semidirect |
| 11. #17989023 | C4 | semidirect |
| 45. #14556531 | C2×C4 | semidirect |
| 60. C2×D8×C73 | C2×C4 | semidirect |
| 193. #1978 | D73 | semidirect |
| 196. C73 | #13022 | semidirect |
| 231. C2×D8 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989023 | 2 |
| #22618808 | 2 |
| C2×#17988393 | 2 |
| C2×#17988388 | 2 |
| #22608041 | 2 |
| #22608020 | 2 |
| C73×#1978 | 2 |
| #13022 | 73 |