Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
284 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 104 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 | C22⋊C4 |
| commutator | C2×C4 | C22×C4×C211 |
| Frattini, cosocle | C42 | C23×C211 |
| prime radical | C22×D4×C211 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C211 ◁ C2×C42×C211 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#97×C211 | C2 | semidirect |
| 3. #329×C211 | C2 | direct (N × H) |
| 13. #97×C211 | C22 | semidirect |
| 60. C2×C211 | #329 | direct (N × H) |
| 63. C211 | C2×#329 | direct (N × H) |
| 64. C2×#329 | C211 | direct (N × H) |
| 66. C2×#97 | C2×C211 | semidirect |
| 67. #329 | C2×C211 | direct (N × H) |
| 77. #97 | C22×C211 | semidirect |
| 124. C2 | #329×C211 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#124×C211 | 2 |
| C2×#97×C211 | 2 |
| #329×C211 | 2 |
| C2×#329 | 211 |