Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
198 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 76 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×C43 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C23×C43 |
| prime radical | C2×#41×C43 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ C22×C4×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#106×C43 | C2 | semidirect |
| 4. C43×#343 | C2 | semidirect |
| 5. C43×#341 | C2 | semidirect |
| 59. #2079 | C43 | direct (N × H) |
| 64. C2×#106 | C2×C43 | semidirect |
| 67. #343 | C2×C43 | semidirect |
| 68. #341 | C2×C43 | semidirect |
| 69. C43 | #2079 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#106×C43 | 2 |
| C43×#417 | 2 |
| C43×#408 | 2 |
| C43×#343 | 2 |
| C43×#341 | 2 |
| #2079 | 43 |