Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
322 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 168 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 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C43 |
| prime radical | C23×C43 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ #117×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C43×#479 | C2 | semidirect |
| 5. C43×#462 | C2 | semidirect |
| 62. #3261 | C43 | direct (N × H) |
| 67. #479 | C2×C43 | semidirect |
| 70. #462 | C2×C43 | semidirect |
| 72. C43 | #3261 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#541 | 2 |
| C43×#479 | 2 |
| C43×#470 | 2 |
| C43×#467 | 2 |
| C43×#462 | 2 |
| C43×#424 | 2 |
| #3261 | 43 |