Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
434 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22590032 | C2 | semidirect |
| 3. #22590031 | C2 | semidirect |
| 4. #22588887 | C2 | semidirect |
| 5. #22588560 | C2 | semidirect |
| 6. #22586462 | C2 | semidirect |
| 7. C71×#1914 | C2 | semidirect |
| 204. #1914 | D71 | semidirect |
| 207. C71 | #13429 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599201 | 2 |
| #22590032 | 2 |
| #22590031 | 2 |
| #22588887 | 2 |
| #22588560 | 2 |
| #22586462 | 2 |
| C71×#1914 | 2 |
| #13429 | 71 |