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 | C2 | (C31⋊C3)⋊#3874 |
| commutator, cosocle, hypocenter | C31×C52⋊C3 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C31 | C3×D3 |
| LCS | G ▷ C31×C52⋊C3 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C52⋊C3×C31⋊C3 | C2 | semidirect |
| 2. (C31⋊C3)⋊#3874 | C2 | direct (N × H) |
| 3. C2×C31⋊#3874 | C3 | semidirect |
| 5. C52⋊C3×C31⋊C3 | C22 | semidirect |
| 7. C2×C31×C52⋊C3 | C2×C3 | semidirect |
| 8. C2×C52×C31⋊C3 | D3 | semidirect |
| 9. C31⋊#3874 | C2×C3 | semidirect |
| 13. C31×C52⋊C3 | C22×C3 | semidirect |
| 14. C52×C31⋊C3 | C2×D3 | semidirect |
| 17. C2×C52×C31 | C3×D3 | semidirect |
| 25. C52×C31 | C2×C3×D3 | semidirect |
| 47. C2×C31⋊C3 | #3874 | semidirect |
| 54. C2×C52⋊C3 | D31⋊C3 | semidirect |
| 60. C31⋊C3 | C2×#3874 | semidirect |
| 63. C52⋊C3 | C2×D31⋊C3 | semidirect |
| 64. C2×C31 | C3×#3874 | semidirect |
| 68. C2×C52 | C3⋊(D31⋊C3) | semidirect |
| 71. C31 | C2×C3×#3874 | semidirect |
| 76. C52 | C2×C3⋊(D31⋊C3) | semidirect |
| 102. C2 | (C31⋊C3)⋊#3874 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52⋊C3×C31⋊C3 | 2 |
| (C31⋊C3)⋊#3874 | 2 |
| C2×C31⋊#3874 | 3 |
| C2×C5×C5⋊(D31⋊C3) | 3 |
| C2×C3⋊(D31⋊C3) | 25 |
| C2×C3×#3874 | 31 |