Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
500 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 500 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. C3×#15688516 | C3 | semidirect |
| 3. #22582554 | C3 | semidirect |
| 5. C3×C37×C32⋊C9 | C3 | semidirect |
| 36. #11758608 | H(3,𝔽3) | semidirect |
| 50. C32×C37 | #731 | semidirect |
| 63. C3×C32⋊C9 | C37⋊C3 | semidirect |
| 86. C37 | #10624745 | semidirect |
| 118. C32 | #15688516 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11758608 | 3 |
| C3×#15688516 | 3 |
| #22582554 | 3 |
| #22582550 | 3 |
| C3×C37×C32⋊C9 | 3 |
| #10624745 | 37 |