Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
520 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 176 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 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C43 |
| prime radical | C43×#392 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C43×#401 | C2 | semidirect |
| 2. C43×#393 | C2 | semidirect |
| 4. C43×#386 | C2 | semidirect |
| 5. C43×#381 | C2 | semidirect |
| 58. #2760 | C43 | direct (N × H) |
| 63. #401 | C2×C43 | semidirect |
| 64. #393 | C2×C43 | semidirect |
| 66. #386 | C2×C43 | semidirect |
| 67. #381 | C2×C43 | semidirect |
| 68. C43 | #2760 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#401 | 2 |
| C43×#393 | 2 |
| C43×#392 | 2 |
| C43×#386 | 2 |
| C43×#381 | 2 |
| #2760 | 43 |