Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
324 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 154. C71 | #11748 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598921 | 2 |
| #22590136 | 2 |
| #22588241 | 2 |
| #22586359 | 2 |
| #22586358 | 2 |
| #22586357 | 2 |
| C71×#1350 | 2 |
| #11748 | 71 |