Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
142 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 25 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 |
|---|---|---|
| 5. #17986379 | C4 | semidirect |
| 8. #17985720 | C4 | semidirect |
| 64. C71 | #7528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22588009 | 2 |
| #22586505 | 2 |
| C71×#1410 | 2 |
| #7528 | 71 |