Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
220 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 58 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. C9×#11758608 | C3 | semidirect |
| 2. #22582538 | C3 | semidirect |
| 3. C37⋊#6862 | C3 | semidirect |
| 4. #22582456 | C3 | semidirect |
| 6. #22582450 | C3 | semidirect |
| 7. #22582449 | C3 | semidirect |
| 94. C37 | #10624587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#11758608 | 3 |
| #22582538 | 3 |
| C37⋊#6862 | 3 |
| #22582456 | 3 |
| #22582451 | 3 |
| #22582450 | 3 |
| #22582449 | 3 |
| #22582445 | 3 |
| C9×H(3,𝔽3)×C37 | 3 |
| #10624587 | 37 |