Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
704 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 73 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. C32×#11758608 | C3 | semidirect |
| 2. C32×C32⋊(C37⋊C3) | C3 | semidirect |
| 3. C3×#15688514 | C3 | semidirect |
| 4. #22582550 | C3 | semidirect |
| 5. C37×#6891 | C3 | semidirect |
| 42. #11758608 | H(3,𝔽3) | semidirect |
| 55. C32×C37 | AΣL(1,𝔽27) | semidirect |
| 70. #6891 | C37⋊C3 | semidirect |
| 96. C37 | #10624743 | semidirect |
| 136. C32 | #15688514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11758608 | 3 |
| C32×C32⋊(C37⋊C3) | 3 |
| C3×#15688514 | 3 |
| #22582550 | 3 |
| C37×#6891 | 3 |
| #10624743 | 37 |