Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
470 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 1. #22623033 | C2 | semidirect |
| 3. C2×#17988400 | C2 | semidirect |
| 4. #22609982 | C2 | semidirect |
| 5. #22608047 | C2 | semidirect |
| 6. #22608035 | C2 | semidirect |
| 7. C73×#2140 | C2 | semidirect |
| 15. #17988854 | C4 | semidirect |
| 170. #2140 | D73 | semidirect |
| 174. C73 | #13068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623033 | 2 |
| C2×#17988854 | 2 |
| C2×#17988400 | 2 |
| #22609982 | 2 |
| #22608047 | 2 |
| #22608035 | 2 |
| C73×#2140 | 2 |
| #13068 | 73 |