Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
944 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 190 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. #22625910 | C2 | semidirect |
| 2. #22625908 | C2 | semidirect |
| 3. #22625907 | C2 | semidirect |
| 4. #22625905 | C2 | semidirect |
| 5. #22625859 | C2 | semidirect |
| 71. C2×D292 | M16 | semidirect |
| 184. C73 | #23356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625910 | 2 |
| #22625908 | 2 |
| #22625907 | 2 |
| #22625905 | 2 |
| #22625859 | 2 |
| #22612495 | 2 |
| #23356 | 73 |