Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
828 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#17988779 | C2 | semidirect |
| 2. #22614847 | C2 | semidirect |
| 3. C2×#17988316 | C2 | semidirect |
| 4. #22607814 | C2 | semidirect |
| 5. C73×#1957 | C2 | semidirect |
| 37. C4⋊#10596831 | D4 | semidirect |
| 45. #127×C73 | D4 | semidirect |
| 59. C2×D292 | D8 | semidirect |
| 179. #1957 | D73 | semidirect |
| 182. C73 | #10228 | semidirect |
| 209. #127 | D292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988779 | 2 |
| #22614847 | 2 |
| C2×#17988316 | 2 |
| #22607814 | 2 |
| C73×#1957 | 2 |
| #10228 | 73 |