Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
360 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 74 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. #22626301 | C2 | semidirect |
| 2. #22625154 | C2 | semidirect |
| 3. #22624895 | C2 | semidirect |
| 4. #22624893 | C2 | semidirect |
| 7. #17989509 | C22 | semidirect |
| 11. #17989428 | C22 | semidirect |
| 12. C8×#10596833 | C22 | semidirect |
| 76. Q16×C73 | M16 | semidirect |
| 80. D8×C73 | M16 | semidirect |
| 130. C73 | #11669 | semidirect |
| 184. Q16 | #11924037 | semidirect |
| 188. D8 | #11924037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626301 | 2 |
| #22625154 | 2 |
| #22624895 | 2 |
| #22624893 | 2 |
| #22618841 | 2 |
| #11669 | 73 |