Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
222 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22590242 | C2 | semidirect |
| 4. #22586318 | C2 | semidirect |
| 6. #22586258 | C2 | semidirect |
| 7. C71×#1370 | C2 | semidirect |
| 80. Dic142 | M32 | semidirect |
| 109. #1370 | D71 | semidirect |
| 113. C71 | #12056 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590242 | 2 |
| #22590171 | 2 |
| C8×#11765854 | 2 |
| #22586318 | 2 |
| #22586294 | 2 |
| #22586258 | 2 |
| C71×#1370 | 2 |
| #12056 | 71 |