Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
316 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22611726 | C2 | semidirect |
| 5. #22610721 | C2 | semidirect |
| 6. #22608035 | C2 | semidirect |
| 7. C73×#2153 | C2 | semidirect |
| 132. #2153 | D73 | semidirect |
| 138. C73 | #13472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611726 | 2 |
| C2×#17988401 | 2 |
| #22610841 | 2 |
| #22610721 | 2 |
| #22608035 | 2 |
| C73×#2153 | 2 |
| #13472 | 73 |