Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
274 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #22608044 | C2 | semidirect |
| 5. #22608031 | C2 | semidirect |
| 6. #22608030 | C2 | semidirect |
| 7. C73×#2161 | C2 | semidirect |
| 133. #2161 | D73 | semidirect |
| 140. C73 | #13497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611558 | 2 |
| #22609987 | 2 |
| #22609978 | 2 |
| #22608044 | 2 |
| #22608031 | 2 |
| #22608030 | 2 |
| C73×#2161 | 2 |
| #13497 | 73 |