Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
442 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 113 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×#17988416 | C2 | semidirect |
| 3. C2×#17988400 | C2 | semidirect |
| 4. C2×#17988399 | C2 | semidirect |
| 5. #22611528 | C2 | semidirect |
| 6. #22610841 | C2 | semidirect |
| 7. C73×#1978 | C2 | semidirect |
| 12. C2×#14556532 | C4 | semidirect |
| 171. #1978 | D73 | semidirect |
| 172. C73 | #13245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556532 | 2 |
| C2×#17988416 | 2 |
| C2×#17988400 | 2 |
| C2×#17988399 | 2 |
| #22611528 | 2 |
| #22610841 | 2 |
| C73×#1978 | 2 |
| #13245 | 73 |