Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
390 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22590094 | C2 | semidirect |
| 3. #346×D71 | C2 | semidirect |
| 4. #22586299 | C2 | semidirect |
| 5. #22586298 | C2 | semidirect |
| 6. #22586297 | C2 | semidirect |
| 7. C71×#1330 | C2 | semidirect |
| 174. #1330 | D71 | semidirect |
| 175. C71 | #11588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597049 | 2 |
| #22590094 | 2 |
| #346×D71 | 2 |
| #22586299 | 2 |
| #22586298 | 2 |
| #22586297 | 2 |
| C71×#1330 | 2 |
| #11588 | 71 |