Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
536 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 98 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. #22626796 | C2 | semidirect |
| 2. #22625232 | C2 | semidirect |
| 3. #22625230 | C2 | semidirect |
| 4. #22625171 | C2 | semidirect |
| 5. #22624771 | C2 | semidirect |
| 6. #22624757 | C2 | semidirect |
| 92. C2×#10596831 | M16 | semidirect |
| 109. C2×D4×C73 | M16 | semidirect |
| 202. C73 | #9093 | semidirect |
| 276. C2×D4 | #11924038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626796 | 2 |
| #22625232 | 2 |
| #22625230 | 2 |
| #22625171 | 2 |
| #22624771 | 2 |
| #22624757 | 2 |
| C2×#17988696 | 2 |
| #9093 | 73 |