Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
386 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22611678 | C2 | semidirect |
| 3. C2×#17988395 | C2 | semidirect |
| 4. C2×#17988370 | C2 | semidirect |
| 5. #22609978 | C2 | semidirect |
| 6. #22608034 | C2 | semidirect |
| 7. C2×#368×C73 | C2 | semidirect |
| 176. C2×#368 | D73 | semidirect |
| 182. C73 | #13392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619652 | 2 |
| #22611678 | 2 |
| C2×#17988395 | 2 |
| C2×#17988370 | 2 |
| #22609978 | 2 |
| #22608034 | 2 |
| C2×#368×C73 | 2 |
| #13392 | 73 |