Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
586 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 105 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×#17986434 | C2 | semidirect |
| 2. C22×#14556069 | C2 | semidirect |
| 3. C2×#17985812 | C2 | semidirect |
| 4. C2×#17985806 | C2 | semidirect |
| 5. #22589250 | C2 | semidirect |
| 6. #22586429 | C2 | semidirect |
| 7. C71×#3155 | C2 | semidirect |
| 37. C2×D568 | D4 | semidirect |
| 43. #14556068 | D4 | semidirect |
| 47. C2×C71⋊C16 | D4 | semidirect |
| 209. #3155 | D71 | semidirect |
| 214. C71 | #13336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986434 | 2 |
| C22×#14556069 | 2 |
| C2×#17985812 | 2 |
| C2×#17985806 | 2 |
| #22589250 | 2 |
| #22586429 | 2 |
| C71×#3155 | 2 |
| #13336 | 71 |