Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
316 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22590138 | C2 | semidirect |
| 3. #334×D71 | C2 | semidirect |
| 4. #22586392 | C2 | semidirect |
| 5. #22586384 | C2 | semidirect |
| 6. #22586382 | C2 | semidirect |
| 7. C71×#1363 | C2 | semidirect |
| 154. #1363 | D71 | semidirect |
| 157. C71 | #11944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598912 | 2 |
| #22590138 | 2 |
| #334×D71 | 2 |
| #22586392 | 2 |
| #22586384 | 2 |
| #22586382 | 2 |
| C71×#1363 | 2 |
| #11944 | 71 |