Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1198 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 1198 conjugacy classes of subgroups — too many to draw. Only its 254 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. #22626123 | C2 | semidirect |
| 28. #14556651 | Q8 | direct (N × H) |
| 62. #11924037 | C2×Q8 | semidirect |
| 117. Q8×C73 | #100 | semidirect |
| 176. C73 | Q8×#100 | semidirect |
| 290. Q8 | #14556651 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11924037 | 2 |
| #22626123 | 2 |
| #22625795 | 2 |
| C4×#14556651 | 2 |
| C2×Q8×C22⋊D73 | 2 |
| Q8×#100 | 73 |