Finite Group DatabasebetaFinite Group DatabasebetaOrder 22599.
488 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 61 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. #21419437 | C3 | semidirect |
| 2. #21419406 | C3 | semidirect |
| 3. #21419402 | C3 | semidirect |
| 4. #21419401 | C3 | semidirect |
| 5. #21419397 | C3 | semidirect |
| 6. #21419397 | C3 | semidirect |
| 7. C3×#14578894 | C3 | semidirect |
| 8. #21419308 | C3 | semidirect |
| 9. C31×#6891 | C3 | semidirect |
| 45. C3×C9×C31 | H(3,𝔽3) | semidirect |
| 61. #11719689 | H(3,𝔽3) | semidirect |
| 97. #6891 | C31⋊C3 | semidirect |
| 128. C31 | #10624749 | semidirect |
| 165. C3×C9 | C32⋊(C31⋊C3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419437 | 3 |
| #21419406 | 3 |
| #21419402 | 3 |
| #21419401 | 3 |
| #21419397 | 3 |
| C3×#14578894 | 3 |
| #21419308 | 3 |
| C31×#6891 | 3 |
| #10624749 | 31 |