Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
708 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 114 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. #22625823 | C2 | semidirect |
| 2. #22625592 | C2 | semidirect |
| 3. #22624751 | C2 | semidirect |
| 4. #22624748 | C2 | semidirect |
| 32. C2×#11924029 | C8 | semidirect |
| 75. C2×D292 | C2×C8 | semidirect |
| 108. C2×Q8×C73 | C2×C8 | semidirect |
| 220. C73 | #7578 | semidirect |
| 280. C2×Q8 | #11924036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625823 | 2 |
| #22625592 | 2 |
| #22624751 | 2 |
| #22624748 | 2 |
| #22612420 | 2 |
| #7578 | 73 |