Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
418 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22611690 | C2 | semidirect |
| 3. C2×#17988400 | C2 | semidirect |
| 4. C2×#17988399 | C2 | semidirect |
| 5. #22610841 | C2 | semidirect |
| 6. #22608024 | C2 | semidirect |
| 7. C73×#1978 | C2 | semidirect |
| 164. #1978 | D73 | semidirect |
| 166. C73 | #13439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556532 | 2 |
| #22611690 | 2 |
| C2×#17988400 | 2 |
| C2×#17988399 | 2 |
| #22610841 | 2 |
| #22608024 | 2 |
| C73×#1978 | 2 |
| #13439 | 73 |