Finite Group DatabasebetaFinite Group DatabasebetaOrder 27900.
128 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #3874⋊D31 |
| commutator, cosocle, hypocenter | C31×C52⋊C3 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C31 | C2×D3 |
| LCS | G ▷ C31×C52⋊C3 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#17987871 | C2 | semidirect |
| 2. C3×C31⋊#3874 | C2 | semidirect |
| 3. C3×C31×#3874 | C2 | semidirect |
| 5. #3874⋊D31 | C3 | direct (N × H) |
| 6. C3×C31×C52⋊C3 | C22 | semidirect |
| 7. C3×C5⋊D155 | D3 | semidirect |
| 11. #17987871 | C2×C3 | semidirect |
| 12. C31⋊#3874 | C2×C3 | semidirect |
| 13. C31×#3874 | C2×C3 | semidirect |
| 16. C31×C52⋊C3 | C22×C3 | semidirect |
| 17. C3×C52×C31 | C2×D3 | semidirect |
| 20. C5⋊D155 | C3×D3 | semidirect |
| 31. C52×C31 | C2×C3×D3 | semidirect |
| 41. C3×#3874 | D31 | semidirect |
| 53. C3×C52⋊C3 | C2×D31 | semidirect |
| 69. #3874 | C3×D31 | semidirect |
| 74. C3×C31 | #3874⋊C2 | semidirect |
| 75. C3×C52 | D3×D31 | semidirect |
| 77. C52⋊C3 | C2×C3×D31 | semidirect |
| 87. C31 | C3×#3874⋊C2 | semidirect |
| 94. C52 | C3×D3×D31 | semidirect |
| 123. C3 | #3874⋊D31 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#17987871 | 2 |
| C3×C31⋊#3874 | 2 |
| C3×C31×#3874 | 2 |
| C3×D5×D155 | 3 |
| #3874⋊D31 | 3 |
| C3×D3×D31 | 25 |
| C3×#3874⋊C2 | 31 |