Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
560 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 85 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. C33×#66524 | C3 | semidirect |
| 2. C3×#15688517 | C3 | semidirect |
| 3. #22582554 | C3 | semidirect |
| 5. C37×#6891 | C3 | semidirect |
| 31. C3×#66524 | H(3,𝔽3) | semidirect |
| 37. C32×C37 | #731 | semidirect |
| 48. #6891 | C37⋊C3 | semidirect |
| 66. C37 | #10624731 | semidirect |
| 88. C32 | #15688517 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#66524 | 3 |
| C3×#15688517 | 3 |
| #22582554 | 3 |
| #22582550 | 3 |
| C37×#6891 | 3 |
| #10624731 | 37 |