Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
142 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C43 | #442 |
| commutator | C8 | C22×C4×C43 |
| Frattini, cosocle | C2×C8 | C23×C43 |
| prime radical | #135×C43 | C22 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C43 ◁ C2×C4×C43 ◁ #97×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C43×#441 | C2 | semidirect |
| 4. C43×#365 | C2 | semidirect |
| 5. C43×#362 | C2 | semidirect |
| 7. C43×#347 | C2 | semidirect |
| 12. Q32×C43 | C4 | semidirect |
| 13. SD32×C43 | C4 | semidirect |
| 61. #2180 | C43 | direct (N × H) |
| 67. #441 | C2×C43 | semidirect |
| 68. #365 | C2×C43 | semidirect |
| 69. #362 | C2×C43 | semidirect |
| 71. #347 | C2×C43 | semidirect |
| 72. C43 | #2180 | direct (N × H) |
| 77. Q32 | C4×C43 | semidirect |
| 78. SD32 | C4×C43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#510 | 2 |
| C43×#444 | 2 |
| C43×#441 | 2 |
| C43×#365 | 2 |
| C43×#362 | 2 |
| C43×#360 | 2 |
| C43×#347 | 2 |
| #2180 | 43 |