Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
296 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22612167 | C2 | semidirect |
| 2. #22612068 | C2 | semidirect |
| 3. #22609459 | C2 | semidirect |
| 4. #22607974 | C2 | semidirect |
| 5. #22607913 | C2 | semidirect |
| 6. #22607898 | C2 | semidirect |
| 154. C73 | #12388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612167 | 2 |
| #22612068 | 2 |
| #22609459 | 2 |
| #22607974 | 2 |
| #22607913 | 2 |
| #22607898 | 2 |
| C73×#3403 | 2 |
| #12388 | 73 |