Finite Group DatabasebetaFinite Group DatabasebetaOrder 27900.
100 conjugacy classes of subgroups; only the 17 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 17 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C31×C52⋊C9 | C22 |
| Frattini | C3 | #3874⋊D31 |
| Fitting, socle | C3×C52×C31 | C2×D3 |
| LCS | G ▷ C31×C52⋊C9 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #28358428 | C2 | semidirect |
| 2. C31⋊#90646 | C2 | semidirect |
| 3. C31×#90646 | C2 | semidirect |
| 5. C31×C52⋊C9 | C22 | semidirect |
| 13. C5⋊D155 | D9 | semidirect |
| 24. C52×C31 | C2×D9 | semidirect |
| 34. #90646 | D31 | semidirect |
| 44. C52⋊C9 | C2×D31 | semidirect |
| 66. C31 | #90646⋊C2 | semidirect |
| 73. C52 | D9×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28358428 | 2 |
| C31⋊#90646 | 2 |
| C31×#90646 | 2 |
| D15⋊D155 | 3 |
| D9×D31 | 25 |
| #90646⋊C2 | 31 |