Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
284 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 61 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. #22590482 | C2 | semidirect |
| 4. #22587869 | C2 | semidirect |
| 6. #22586323 | C2 | semidirect |
| 7. C71×#1334 | C2 | semidirect |
| 147. #1334 | D71 | semidirect |
| 148. C71 | #12389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601417 | 2 |
| #22590577 | 2 |
| #22590482 | 2 |
| #22587869 | 2 |
| #22586382 | 2 |
| #22586323 | 2 |
| C71×#1334 | 2 |
| #12389 | 71 |