Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
386 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22589116 | C2 | semidirect |
| 3. #22587021 | C2 | semidirect |
| 6. #22586190 | C2 | semidirect |
| 7. C2×#332×C71 | C2 | semidirect |
| 177. C2×#332 | D71 | semidirect |
| 180. C71 | #10552 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598736 | 2 |
| #22589116 | 2 |
| #22587021 | 2 |
| #22587015 | 2 |
| #22586738 | 2 |
| #22586190 | 2 |
| C2×#332×C71 | 2 |
| #10552 | 71 |