Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
560 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 280 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 | C22×D4×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 |
|---|---|---|
| 2. #391×C211 | C2 | semidirect |
| 3. #388×C211 | C2 | semidirect |
| 5. C4×C22⋊C4×C211 | C2 | semidirect |
| 6. #376×C211 | C2 | semidirect |
| 10. #124×C211 | C4 | semidirect |
| 25. C2×Q8×C211 | C2×C4 | semidirect |
| 39. C22⋊C4×C211 | C2×C4 | semidirect |
| 42. C42×C211 | C2×C4 | semidirect |
| 85. C211 | #2372 | direct (N × H) |
| 86. #2372 | C211 | direct (N × H) |
| 88. #391 | C2×C211 | semidirect |
| 89. #388 | C2×C211 | semidirect |
| 91. C4×C22⋊C4 | C2×C211 | semidirect |
| 92. #376 | C2×C211 | semidirect |
| 96. #124 | C4×C211 | semidirect |
| 111. C2×Q8 | C2×C4×C211 | semidirect |
| 125. C22⋊C4 | C2×C4×C211 | semidirect |
| 128. C42 | C2×C4×C211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#124×C211 | 2 |
| #391×C211 | 2 |
| #388×C211 | 2 |
| #386×C211 | 2 |
| C4×C22⋊C4×C211 | 2 |
| #376×C211 | 2 |
| #2372 | 211 |