Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
550 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22599468 | C2 | semidirect |
| 3. #22598736 | C2 | semidirect |
| 4. #22589258 | C2 | semidirect |
| 5. #22586834 | C2 | semidirect |
| 6. #22586190 | C2 | semidirect |
| 7. C71×#1981 | C2 | semidirect |
| 204. #1981 | D71 | semidirect |
| 208. C71 | #10200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599650 | 2 |
| #22599468 | 2 |
| #22598736 | 2 |
| #22589258 | 2 |
| #22586834 | 2 |
| #22586190 | 2 |
| C71×#1981 | 2 |
| #10200 | 71 |