Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
484 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C211 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C211 |
| prime radical | C2×#127×C211 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C211 ◁ C2×C42×C211 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #533×C211 | C2 | semidirect |
| 3. #490×C211 | C2 | semidirect |
| 4. #486×C211 | C2 | semidirect |
| 5. #418×C211 | C2 | semidirect |
| 6. C4×M16×C211 | C2 | semidirect |
| 10. C4⋊Q8×C211 | C22 | semidirect |
| 14. #125×C211 | C22 | semidirect |
| 19. #102×C211 | C22 | semidirect |
| 20. #97×C211 | C22 | semidirect |
| 21. C4×C8×C211 | C22 | semidirect |
| 74. C211 | #3138 | direct (N × H) |
| 75. #3138 | C211 | direct (N × H) |
| 76. #533 | C2×C211 | semidirect |
| 78. #490 | C2×C211 | semidirect |
| 79. #486 | C2×C211 | semidirect |
| 80. #418 | C2×C211 | semidirect |
| 81. C4×M16 | C2×C211 | semidirect |
| 85. C4⋊Q8 | C22×C211 | semidirect |
| 89. #125 | C22×C211 | semidirect |
| 94. #102 | C22×C211 | semidirect |
| 95. #97 | C22×C211 | semidirect |
| 96. C4×C8 | C22×C211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #533×C211 | 2 |
| C2×#127×C211 | 2 |
| #490×C211 | 2 |
| #486×C211 | 2 |
| #418×C211 | 2 |
| C4×M16×C211 | 2 |
| #3138 | 211 |