Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1314 conjugacy classes of subgroups; only the 240 normal subgroups are shown.
This group has 1314 conjugacy classes of subgroups — too many to draw. Only its 240 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. Q8×#11924037 | C2 | semidirect |
| 2. #22626073 | C2 | semidirect |
| 3. #22625795 | C2 | semidirect |
| 4. C4×#14556651 | C2 | semidirect |
| 62. #11924037 | #41 | semidirect |
| 116. Q8×C73 | #100 | semidirect |
| 178. C73 | #22536 | semidirect |
| 289. Q8 | #14556651 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11924037 | 2 |
| #22626073 | 2 |
| #22625795 | 2 |
| C4×#14556651 | 2 |
| C2×#17989256 | 2 |
| #22536 | 73 |