Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
650 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 650 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. #22599255 | C2 | semidirect |
| 2. #22589164 | C2 | semidirect |
| 3. #22586900 | C2 | semidirect |
| 4. #22586185 | C2 | semidirect |
| 5. C71×#3150 | C2 | semidirect |
| 76. C2×C8×C71 | D8 | semidirect |
| 138. #3150 | D71 | semidirect |
| 142. C71 | #10218 | semidirect |
| 212. C2×C8 | #11765850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599255 | 2 |
| #22589164 | 2 |
| #22586900 | 2 |
| #22586185 | 2 |
| C71×#3150 | 2 |
| #10218 | 71 |