Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
206 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 64 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 | #447 |
| commutator, Frattini, cosocle | C2×C8 | C23×C43 |
| prime radical | C43×#578 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C43 ◁ C2×C4×C43 ◁ #131×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C43×#510 | C2 | semidirect |
| 3. C2×Q32×C43 | C2 | semidirect |
| 4. C43×#473 | C2 | semidirect |
| 5. C43×#362 | C2 | semidirect |
| 6. C43×#359 | C2 | semidirect |
| 7. C43×#350 | C2 | semidirect |
| 84. #2195 | C43 | direct (N × H) |
| 90. #510 | C2×C43 | semidirect |
| 91. C2×Q32 | C2×C43 | semidirect |
| 92. #473 | C2×C43 | semidirect |
| 93. #362 | C2×C43 | semidirect |
| 94. #359 | C2×C43 | semidirect |
| 95. #350 | C2×C43 | semidirect |
| 96. C43 | #2195 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#578 | 2 |
| C43×#510 | 2 |
| C2×Q32×C43 | 2 |
| C43×#473 | 2 |
| C43×#362 | 2 |
| C43×#359 | 2 |
| C43×#350 | 2 |
| #2195 | 43 |