Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
588 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22617924 | C2 | semidirect |
| 4. #22607756 | C2 | semidirect |
| 5. C73×#1272 | C2 | semidirect |
| 52. C2×Dic146 | SD16 | semidirect |
| 79. C2×Q8×C73 | SD16 | semidirect |
| 158. #1272 | D73 | semidirect |
| 159. C73 | #7749 | semidirect |
| 210. C2×Q8 | #11924017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22617924 | 2 |
| #22611021 | 2 |
| #22611018 | 2 |
| #22607756 | 2 |
| C73×#1272 | 2 |
| #7749 | 73 |