Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
504 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 2. #22625233 | C2 | semidirect |
| 4. #22625174 | C2 | semidirect |
| 5. #22624771 | C2 | semidirect |
| 6. #22624757 | C2 | semidirect |
| 103. C2×Q8×C73 | M16 | semidirect |
| 115. C2×C8×C73 | M16 | semidirect |
| 192. C73 | #9091 | semidirect |
| 259. C2×Q8 | #11924037 | semidirect |
| 286. C2×C8 | #11924037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626793 | 2 |
| #22625233 | 2 |
| #22625230 | 2 |
| #22625174 | 2 |
| #22624771 | 2 |
| #22624757 | 2 |
| C2×#17988688 | 2 |
| #9091 | 73 |