Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
184 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 60 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 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C43 |
| prime radical | C2×D4×C43 | D4 |
| 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 |
|---|---|---|
| 2. C43×#501 | C2 | semidirect |
| 3. C43×#491 | C2 | semidirect |
| 5. C43×#330 | C2 | semidirect |
| 6. C43×#330 | C2 | semidirect |
| 85. #1664 | C43 | direct (N × H) |
| 91. #501 | C2×C43 | semidirect |
| 92. #491 | C2×C43 | semidirect |
| 94. #330 | C2×C43 | semidirect |
| 95. #330 | C2×C43 | semidirect |
| 97. C43 | #1664 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#563 | 2 |
| C43×#501 | 2 |
| C43×#491 | 2 |
| C43×#489 | 2 |
| C43×#330 | 2 |
| C43×#329 | 2 |
| #1664 | 43 |