Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
328 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#17988407 | C2 | semidirect |
| 4. C2×#17988365 | C2 | semidirect |
| 6. #22608012 | C2 | semidirect |
| 7. C73×#1375 | C2 | semidirect |
| 156. #1375 | D73 | semidirect |
| 157. C73 | #13128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988407 | 2 |
| C2×#17988368 | 2 |
| C2×#17988365 | 2 |
| #22609716 | 2 |
| #22608012 | 2 |
| C73×#1375 | 2 |
| #13128 | 73 |