Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
612 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 94 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. D4×#11924037 | C2 | semidirect |
| 2. #22626073 | C2 | semidirect |
| 3. #22625438 | C2 | semidirect |
| 4. #22625256 | C2 | semidirect |
| 5. #22624801 | C2 | semidirect |
| 6. #22624776 | C2 | semidirect |
| 95. #11924037 | D8 | semidirect |
| 182. D4×C73 | #100 | semidirect |
| 275. C73 | #9253 | semidirect |
| 459. D4 | #14556651 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#11924037 | 2 |
| #22626073 | 2 |
| #22625438 | 2 |
| #22625256 | 2 |
| #22624801 | 2 |
| #22624776 | 2 |
| C2×#17988780 | 2 |
| #9253 | 73 |