Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
256 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 96 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×C43 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C43 |
| prime radical | C24×C43 | D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C43 ◁ C23×C4×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#107×C43 | C2 | semidirect |
| 4. C43×#340 | C2 | semidirect |
| 5. C43×#340 | C2 | semidirect |
| 72. #2075 | C43 | direct (N × H) |
| 79. C2×#107 | C2×C43 | semidirect |
| 82. #340 | C2×C43 | semidirect |
| 83. #340 | C2×C43 | semidirect |
| 84. C43 | #2075 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#107×C43 | 2 |
| C2×C22⋊C8×C43 | 2 |
| C43×#380 | 2 |
| C43×#340 | 2 |
| #2075 | 43 |