Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
412 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 93 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×#17988399 | C2 | semidirect |
| 4. C2×#17988387 | C2 | semidirect |
| 5. #22611545 | C2 | semidirect |
| 6. #22608039 | C2 | semidirect |
| 7. C73×#1816 | C2 | semidirect |
| 176. #1816 | D73 | semidirect |
| 178. C73 | #13393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988857 | 2 |
| C2×#17988416 | 2 |
| C2×#17988399 | 2 |
| C2×#17988387 | 2 |
| #22611545 | 2 |
| #22608039 | 2 |
| C73×#1816 | 2 |
| #13393 | 73 |