Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
528 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 528 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 | C23×C43 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C43 |
| prime radical | C2×#121×C43 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C22⋊Q8×C43 | C2 | semidirect |
| 3. C43×#399 | C2 | semidirect |
| 4. C43×#398 | C2 | semidirect |
| 5. C43×#394 | C2 | semidirect |
| 6. C43×#394 | C2 | semidirect |
| 7. C43×#393 | C2 | semidirect |
| 8. C43×#381 | C2 | semidirect |
| 97. #2816 | C43 | direct (N × H) |
| 104. C2×C22⋊Q8 | C2×C43 | semidirect |
| 106. #399 | C2×C43 | semidirect |
| 107. #398 | C2×C43 | semidirect |
| 108. #394 | C2×C43 | semidirect |
| 109. #394 | C2×C43 | semidirect |
| 110. #393 | C2×C43 | semidirect |
| 111. #381 | C2×C43 | semidirect |
| 112. C43 | #2816 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊Q8×C43 | 2 |
| C2×#121×C43 | 2 |
| C43×#399 | 2 |
| C43×#398 | 2 |
| C43×#394 | 2 |
| C43×#393 | 2 |
| C43×#381 | 2 |
| #2816 | 43 |