Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
390 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 2. #22625872 | C2 | semidirect |
| 3. #22625509 | C2 | semidirect |
| 5. #22624817 | C2 | semidirect |
| 6. #22624763 | C2 | semidirect |
| 110. D4×C73 | #108 | semidirect |
| 175. C73 | #8898 | semidirect |
| 281. D4 | #14556662 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626859 | 2 |
| #22625872 | 2 |
| #22625509 | 2 |
| #22625267 | 2 |
| #22624817 | 2 |
| #22624763 | 2 |
| #22608310 | 2 |
| #8898 | 73 |