Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
414 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 414 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 |
|---|---|---|
| 1. #22582680 | C3 | semidirect |
| 2. #22582647 | C3 | semidirect |
| 3. #22582643 | C3 | semidirect |
| 4. #22582639 | C3 | semidirect |
| 5. #22582639 | C3 | semidirect |
| 6. C3×#15688520 | C3 | semidirect |
| 7. C3×#15688518 | C3 | semidirect |
| 8. C3×#15688517 | C3 | semidirect |
| 9. C37×#6910 | C3 | semidirect |
| 84. #6910 | C37⋊C3 | semidirect |
| 117. C37 | #10624763 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582680 | 3 |
| #22582647 | 3 |
| #22582643 | 3 |
| #22582639 | 3 |
| C3×#15688520 | 3 |
| C3×#15688518 | 3 |
| C3×#15688517 | 3 |
| C37×#6910 | 3 |
| #10624763 | 37 |