Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
502 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 139 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×#17988415 | C2 | semidirect |
| 3. C2×#17988389 | C2 | semidirect |
| 4. #22610797 | C2 | semidirect |
| 5. C2×#346×C73 | C2 | semidirect |
| 9. C2×D1168 | C4 | semidirect |
| 72. C16×C73 | C22⋊C4 | semidirect |
| 122. C2×#346 | D73 | semidirect |
| 124. C73 | #13239 | semidirect |
| 191. C16 | #11924005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1168 | 2 |
| C2×#17988415 | 2 |
| C2×#17988389 | 2 |
| #22610797 | 2 |
| C2×#346×C73 | 2 |
| #13239 | 73 |