Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
542 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22598862 | C2 | semidirect |
| 5. #22586903 | C2 | semidirect |
| 6. #22586184 | C2 | semidirect |
| 7. C71×#1518 | C2 | semidirect |
| 94. C2×C71⋊C8 | SD16 | semidirect |
| 192. #1518 | D71 | semidirect |
| 194. C71 | #10220 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599283 | 2 |
| #22599278 | 2 |
| #22598862 | 2 |
| #22589163 | 2 |
| #22586903 | 2 |
| #22586184 | 2 |
| C71×#1518 | 2 |
| #10220 | 71 |