Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
364 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22611733 | C2 | semidirect |
| 3. #22611728 | C2 | semidirect |
| 4. #22607887 | C2 | semidirect |
| 5. D4⋊#11924003 | C2 | semidirect |
| 6. #22607885 | C2 | semidirect |
| 7. C73×D4⋊C16 | C2 | semidirect |
| 176. D4⋊C16 | D73 | semidirect |
| 177. C73 | #11632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618638 | 2 |
| #22611733 | 2 |
| #22611728 | 2 |
| #22607887 | 2 |
| D4⋊#11924003 | 2 |
| #22607885 | 2 |
| C73×D4⋊C16 | 2 |
| #11632 | 73 |