Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
348 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22590538 | C2 | semidirect |
| 3. #22590521 | C2 | semidirect |
| 4. #22589763 | C2 | semidirect |
| 5. #22586353 | C2 | semidirect |
| 6. #22586350 | C2 | semidirect |
| 7. C71×#1314 | C2 | semidirect |
| 175. #1314 | D71 | semidirect |
| 176. C71 | #12280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599133 | 2 |
| #22590538 | 2 |
| #22590521 | 2 |
| #22589763 | 2 |
| #22586353 | 2 |
| #22586350 | 2 |
| C71×#1314 | 2 |
| #12280 | 71 |