Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
166 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 166 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 | C22×C43 | #121 |
| 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 |
|---|---|---|
| 1. C43×#498 | C2 | semidirect |
| 5. C43×#334 | C2 | semidirect |
| 6. C43×#333 | C2 | semidirect |
| 7. C43×#332 | C2 | semidirect |
| 59. C8×C43 | SD16 | semidirect |
| 72. #1671 | C43 | direct (N × H) |
| 77. #498 | C2×C43 | semidirect |
| 81. #334 | C2×C43 | semidirect |
| 82. #333 | C2×C43 | semidirect |
| 83. #332 | C2×C43 | semidirect |
| 84. C43 | #1671 | direct (N × H) |
| 136. C8 | SD16×C43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#498 | 2 |
| C43×#476 | 2 |
| C43×#461 | 2 |
| C8×D4×C43 | 2 |
| C43×#334 | 2 |
| C43×#333 | 2 |
| C43×#332 | 2 |
| #1671 | 43 |