Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
754 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22610921 | C2 | semidirect |
| 3. #22608664 | C2 | semidirect |
| 4. #22608522 | C2 | semidirect |
| 5. #22608371 | C2 | semidirect |
| 6. #22608368 | C2 | semidirect |
| 7. C73×#1966 | C2 | semidirect |
| 237. #1966 | D73 | semidirect |
| 242. C73 | #8470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623844 | 2 |
| #22610921 | 2 |
| #22608664 | 2 |
| #22608522 | 2 |
| #22608371 | 2 |
| #22608368 | 2 |
| C73×#1966 | 2 |
| #8470 | 73 |