Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
488 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 70 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. #22582648 | C3 | semidirect |
| 2. #22582644 | C3 | semidirect |
| 3. #22582643 | C3 | semidirect |
| 4. #22582639 | C3 | semidirect |
| 5. #22582638 | C3 | semidirect |
| 6. C3×#15688514 | C3 | semidirect |
| 7. #22582551 | C3 | semidirect |
| 8. (C3×C37⋊C3)⋊H(3,𝔽3) | C3 | semidirect |
| 9. C37×3−1+4 | C3 | semidirect |
| 44. 3−1+2×C37 | H(3,𝔽3) | semidirect |
| 49. C3×C9×C37 | H(3,𝔽3) | semidirect |
| 89. 3−1+4 | C37⋊C3 | semidirect |
| 127. C37 | #10624749 | semidirect |
| 148. 3−1+2 | C32⋊(C37⋊C3) | semidirect |
| 163. C3×C9 | C32⋊(C37⋊C3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582648 | 3 |
| #22582644 | 3 |
| #22582643 | 3 |
| #22582639 | 3 |
| #22582638 | 3 |
| C3×#15688514 | 3 |
| #22582551 | 3 |
| (C3×C37⋊C3)⋊H(3,𝔽3) | 3 |
| C37×3−1+4 | 3 |
| #10624749 | 37 |