Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
274 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 55 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. #22612249 | C2 | semidirect |
| 3. #22612053 | C2 | semidirect |
| 4. #22608124 | C2 | semidirect |
| 5. #22608116 | C2 | semidirect |
| 6. #22608072 | C2 | semidirect |
| 7. C2×Q64×C73 | C2 | semidirect |
| 119. C2×Q64 | D73 | semidirect |
| 124. C73 | #13672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623080 | 2 |
| #22612249 | 2 |
| #22612053 | 2 |
| #22608124 | 2 |
| #22608116 | 2 |
| #22608072 | 2 |
| C2×Q64×C73 | 2 |
| #13672 | 73 |