Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
358 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 184 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 ◁ C2×C42×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C43×#498 | C2 | semidirect |
| 3. C43×#494 | C2 | semidirect |
| 4. C43×#487 | C2 | semidirect |
| 6. C43×#441 | C2 | semidirect |
| 65. #3185 | C43 | direct (N × H) |
| 70. #498 | C2×C43 | semidirect |
| 71. #494 | C2×C43 | semidirect |
| 72. #487 | C2×C43 | semidirect |
| 74. #441 | C2×C43 | semidirect |
| 76. C43 | #3185 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#533 | 2 |
| C43×#498 | 2 |
| C43×#494 | 2 |
| C43×#487 | 2 |
| C43×#470 | 2 |
| C43×#441 | 2 |
| C4×M16×C43 | 2 |
| #3185 | 43 |