Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
500 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 82 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. C3×#15688517 | C3 | semidirect |
| 2. #22582554 | C3 | semidirect |
| 4. C3×C32⋊#66524 | C3 | semidirect |
| 5. C32×3−1+2×C37 | C3 | semidirect |
| 30. 3−1+2×C37 | H(3,𝔽3) | semidirect |
| 50. C32×C37 | #731 | semidirect |
| 59. C32×3−1+2 | C37⋊C3 | semidirect |
| 86. C37 | #10624745 | semidirect |
| 97. 3−1+2 | C32⋊(C37⋊C3) | semidirect |
| 118. C32 | #15688517 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688517 | 3 |
| #22582554 | 3 |
| #22582550 | 3 |
| C3×C32⋊#66524 | 3 |
| C32×3−1+2×C37 | 3 |
| #10624745 | 37 |