Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
944 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 198 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. #22625911 | C2 | semidirect |
| 2. #22625909 | C2 | semidirect |
| 3. #22625906 | C2 | semidirect |
| 4. #22625904 | C2 | semidirect |
| 5. #22625859 | C2 | semidirect |
| 100. C2×D4×C73 | M16 | semidirect |
| 184. C73 | #23356 | semidirect |
| 248. C2×D4 | #11924038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625911 | 2 |
| #22625909 | 2 |
| #22625906 | 2 |
| #22625904 | 2 |
| #22625859 | 2 |
| #22612495 | 2 |
| #23356 | 73 |