Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
238 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 238 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 |
|---|---|---|
| 93. #66524 | #733 | semidirect |
| 140. C37 | #10624787 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688520 | 3 |
| #22582574 | 3 |
| #22582573 | 3 |
| #22582568 | 3 |
| C3×C9×#66524 | 3 |
| #22582481 | 3 |
| #22582480 | 3 |
| 3−1+2⋊#66524 | 3 |
| #22582478 | 3 |
| #22582471 | 3 |
| C37×3−1+2⋊C9 | 3 |
| #10624787 | 37 |