Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
816 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 360 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C211 | C24 |
| commutator | C22 | C23×C4×C211 |
| Frattini, cosocle | C23 | C24×C211 |
| prime radical | C25×C211 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C211 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #385×C211 | C2 | semidirect |
| 4. #380×C211 | C2 | semidirect |
| 8. C2×C4⋊C4×C211 | C22 | semidirect |
| 10. C2×C22⋊C4×C211 | C4 | semidirect |
| 14. #95×C211 | C22 | semidirect |
| 24. C22×C4×C211 | C2×C4 | semidirect |
| 30. C22⋊C4×C211 | C2×C4 | semidirect |
| 36. C23×C211 | C4⋊C4 | semidirect |
| 71. C211 | #2315 | direct (N × H) |
| 72. #2315 | C211 | direct (N × H) |
| 75. #385 | C2×C211 | semidirect |
| 76. #380 | C2×C211 | semidirect |
| 80. C2×C4⋊C4 | C22×C211 | semidirect |
| 82. C2×C22⋊C4 | C4×C211 | semidirect |
| 86. #95 | C22×C211 | semidirect |
| 96. C22×C4 | C2×C4×C211 | semidirect |
| 102. C22⋊C4 | C2×C4×C211 | semidirect |
| 108. C23 | C4⋊C4×C211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊C4×C211 | 2 |
| #385×C211 | 2 |
| #380×C211 | 2 |
| #2315 | 211 |