Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1218 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1218 conjugacy classes of subgroups — too many to draw. Only its 219 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. C22×#14556120 | C2 | semidirect |
| 2. C2×#17986364 | C2 | semidirect |
| 4. #22589487 | C2 | semidirect |
| 5. #22589309 | C2 | semidirect |
| 6. #22588655 | C2 | semidirect |
| 7. C71×#1749 | C2 | semidirect |
| 35. #14556120 | D4 | semidirect |
| 137. C22×C71 | #490 | semidirect |
| 168. #1749 | D71 | semidirect |
| 169. C71 | #25913 | semidirect |
| 304. C22 | #17986364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556120 | 2 |
| C2×#17986364 | 2 |
| #22596685 | 2 |
| #22589487 | 2 |
| #22589309 | 2 |
| #22588655 | 2 |
| C71×#1749 | 2 |
| #25913 | 71 |