Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
550 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 550 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 |
|---|---|---|
| 3. C2×#17986209 | C2 | semidirect |
| 4. #22587011 | C2 | semidirect |
| 6. #22586236 | C2 | semidirect |
| 7. C71×#1461 | C2 | semidirect |
| 213. #1461 | D71 | semidirect |
| 215. C71 | #10185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599463 | 2 |
| #22597812 | 2 |
| C2×#17986209 | 2 |
| #22587011 | 2 |
| #22586740 | 2 |
| #22586236 | 2 |
| C71×#1461 | 2 |
| #10185 | 71 |