Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
400 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22590129 | C2 | semidirect |
| 3. C2×#17985827 | C2 | semidirect |
| 6. #22586450 | C2 | semidirect |
| 7. C71×#1382 | C2 | semidirect |
| 21. #17985782 | C4 | semidirect |
| 42. #14556068 | C2×C4 | semidirect |
| 57. C2×C16×C71 | C2×C4 | semidirect |
| 164. #1382 | D71 | semidirect |
| 165. C71 | #12926 | semidirect |
| 207. C2×C16 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596937 | 2 |
| #22590129 | 2 |
| C2×#17985827 | 2 |
| C2×#17985782 | 2 |
| #22588401 | 2 |
| #22586450 | 2 |
| C71×#1382 | 2 |
| #12926 | 71 |