Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
492 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22589283 | C2 | semidirect |
| 4. #22586890 | C2 | semidirect |
| 5. #22586204 | C2 | semidirect |
| 6. #22586196 | C2 | semidirect |
| 9. #17986394 | C4 | semidirect |
| 10. #17986358 | C4 | semidirect |
| 34. #14556128 | C2×C4 | semidirect |
| 35. #14556128 | C2×C4 | semidirect |
| 50. #14556039 | C2×C4 | semidirect |
| 212. C71 | #9379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599343 | 2 |
| #22589283 | 2 |
| #22586938 | 2 |
| #22586890 | 2 |
| #22586204 | 2 |
| #22586196 | 2 |
| C71×#2337 | 2 |
| #9379 | 71 |