Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
220 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 220 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 |
| 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 |
|---|---|---|
| 1. C43×#576 | C2 | semidirect |
| 2. C43×#509 | C2 | semidirect |
| 3. C2×D16×C43 | C2 | semidirect |
| 4. C43×#472 | C2 | semidirect |
| 5. C43×#361 | C2 | semidirect |
| 6. C43×#359 | C2 | semidirect |
| 7. C43×#350 | C2 | semidirect |
| 16. C2×D8×C43 | C22 | semidirect |
| 21. M32×C43 | C22 | semidirect |
| 22. C2×C16×C43 | C22 | semidirect |
| 23. #108×C43 | C22 | semidirect |
| 87. #2192 | C43 | direct (N × H) |
| 94. #576 | C2×C43 | semidirect |
| 95. #509 | C2×C43 | semidirect |
| 96. C2×D16 | C2×C43 | semidirect |
| 97. #472 | C2×C43 | semidirect |
| 98. #361 | C2×C43 | semidirect |
| 99. #359 | C2×C43 | semidirect |
| 100. #350 | C2×C43 | semidirect |
| 101. C43 | #2192 | direct (N × H) |
| 110. C2×D8 | C22×C43 | semidirect |
| 115. M32 | C22×C43 | semidirect |
| 116. C2×C16 | C22×C43 | semidirect |
| 117. #108 | C22×C43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#576 | 2 |
| C43×#509 | 2 |
| C2×D16×C43 | 2 |
| C43×#472 | 2 |
| C43×#361 | 2 |
| C43×#359 | 2 |
| C43×#350 | 2 |
| #2192 | 43 |