Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
620 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 620 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. #22612839 | C2 | semidirect |
| 3. #22608490 | C2 | semidirect |
| 4. #22608427 | C2 | semidirect |
| 5. #22608321 | C2 | semidirect |
| 6. #22607832 | C2 | semidirect |
| 7. C73×#1286 | C2 | semidirect |
| 13. #17988793 | C4 | semidirect |
| 14. #17988783 | C4 | semidirect |
| 37. #14556591 | C2×C4 | semidirect |
| 38. #14556588 | C2×C4 | semidirect |
| 69. C4⋊C8×C73 | C2×C4 | semidirect |
| 221. #1286 | D73 | semidirect |
| 222. C73 | #9179 | semidirect |
| 277. C4⋊C8 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619397 | 2 |
| #22612839 | 2 |
| #22608490 | 2 |
| #22608427 | 2 |
| #22608321 | 2 |
| #22607832 | 2 |
| C73×#1286 | 2 |
| #9179 | 73 |