Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
456 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#17988403 | C2 | semidirect |
| 4. #22610847 | C2 | semidirect |
| 5. #22608035 | C2 | semidirect |
| 6. #22608016 | C2 | semidirect |
| 24. C2×Q32×C73 | C4 | semidirect |
| 25. C2×SD32×C73 | C4 | semidirect |
| 173. C73 | #13035 | semidirect |
| 179. C2×Q32 | Dic73 | semidirect |
| 180. C2×SD32 | Dic73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618848 | 2 |
| C2×#17988403 | 2 |
| #22611659 | 2 |
| #22610847 | 2 |
| #22608035 | 2 |
| #22608016 | 2 |
| C2×#510×C73 | 2 |
| #13035 | 73 |