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. #21419438 | C3 | semidirect |
| 2. #21419405 | C3 | semidirect |
| 3. #21419400 | C3 | semidirect |
| 4. #21419400 | C3 | semidirect |
| 5. #21419396 | C3 | semidirect |
| 6. #21419395 | C3 | semidirect |
| 7. C3×#14578894 | C3 | semidirect |
| 8. #21419312 | C3 | semidirect |
| 9. C31×C32⋊H(3,𝔽3) | C3 | semidirect |
| 60. #11719689 | H(3,𝔽3) | semidirect |
| 65. C3×C31⋊C9 | H(3,𝔽3) | semidirect |
| 97. C32⋊H(3,𝔽3) | C31⋊C3 | semidirect |
| 127. C31 | #10624749 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21419438 | 3 |
| #21419405 | 3 |
| #21419400 | 3 |
| #21419396 | 3 |
| #21419395 | 3 |
| C3×#14578894 | 3 |
| #21419312 | 3 |
| C31×C32⋊H(3,𝔽3) | 3 |
| #10624749 | 31 |