Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
348 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22612129 | C2 | semidirect |
| 3. #22612112 | C2 | semidirect |
| 4. #22611354 | C2 | semidirect |
| 5. #22607944 | C2 | semidirect |
| 6. #22607941 | C2 | semidirect |
| 7. C73×#1314 | C2 | semidirect |
| 175. #1314 | D73 | semidirect |
| 176. C73 | #12280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620724 | 2 |
| #22612129 | 2 |
| #22612112 | 2 |
| #22611354 | 2 |
| #22607944 | 2 |
| #22607941 | 2 |
| C73×#1314 | 2 |
| #12280 | 73 |