Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
488 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 488 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. #22597479 | C2 | semidirect |
| 3. #22589138 | C2 | semidirect |
| 4. #22586784 | C2 | semidirect |
| 5. #22586239 | C2 | semidirect |
| 6. #22586191 | C2 | semidirect |
| 7. C71×#1524 | C2 | semidirect |
| 231. #1524 | D71 | semidirect |
| 235. C71 | #9052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598383 | 2 |
| #22597479 | 2 |
| #22589138 | 2 |
| #22586784 | 2 |
| #22586239 | 2 |
| #22586191 | 2 |
| C71×#1524 | 2 |
| #9052 | 71 |