Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
504 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22611260 | C2 | semidirect |
| 4. #22611033 | C2 | semidirect |
| 5. #22607756 | C2 | semidirect |
| 6. #22607755 | C2 | semidirect |
| 105. C2×D4×C73 | Q16 | semidirect |
| 214. C73 | #7756 | semidirect |
| 284. C2×D4 | Dic292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22616948 | 2 |
| #22611260 | 2 |
| #22611067 | 2 |
| #22611033 | 2 |
| #22607756 | 2 |
| #22607755 | 2 |
| C73×#1270 | 2 |
| #7756 | 73 |