Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
152 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C43 | #121 |
| commutator, Frattini, cosocle | C42 | C23×C43 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ C42×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 42. C8×C43 | Q16 | semidirect |
| 51. #1694 | C43 | direct (N × H) |
| 60. C43 | #1694 | direct (N × H) |
| 97. C8 | Q16×C43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#500 | 2 |
| C43×#462 | 2 |
| C43×#446 | 2 |
| C43×#334 | 2 |
| C43×#332 | 2 |
| #1694 | 43 |