Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. #22587112 | C2 | semidirect |
| 4. #22586995 | C2 | semidirect |
| 5. #22586903 | C2 | semidirect |
| 7. C71×#1286 | C2 | semidirect |
| 179. #1286 | D71 | semidirect |
| 180. C71 | #10468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598139 | 2 |
| #22588347 | 2 |
| #22587112 | 2 |
| #22586995 | 2 |
| #22586903 | 2 |
| #22586660 | 2 |
| C71×#1286 | 2 |
| #10468 | 71 |