Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
316 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 3. #22589829 | C2 | semidirect |
| 4. #22586352 | C2 | semidirect |
| 6. #22586279 | C2 | semidirect |
| 7. C71×#2235 | C2 | semidirect |
| 154. #2235 | D71 | semidirect |
| 160. C71 | #12290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599693 | 2 |
| #22590520 | 2 |
| #22589829 | 2 |
| #22586352 | 2 |
| #22586350 | 2 |
| #22586279 | 2 |
| C71×#2235 | 2 |
| #12290 | 71 |