Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
446 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 446 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 | C22×C43 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C43 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C43×#532 | C2 | semidirect |
| 2. C43×#498 | C2 | semidirect |
| 3. C43×#493 | C2 | semidirect |
| 4. C43×#486 | C2 | semidirect |
| 5. C43×#469 | C2 | semidirect |
| 6. C43×#442 | C2 | semidirect |
| 7. C4×M16×C43 | C2 | semidirect |
| 60. C8×C43 | #41 | semidirect |
| 72. #3184 | C43 | direct (N × H) |
| 77. #532 | C2×C43 | semidirect |
| 78. #498 | C2×C43 | semidirect |
| 79. #493 | C2×C43 | semidirect |
| 80. #486 | C2×C43 | semidirect |
| 81. #469 | C2×C43 | semidirect |
| 82. #442 | C2×C43 | semidirect |
| 83. C4×M16 | C2×C43 | semidirect |
| 84. C43 | #3184 | direct (N × H) |
| 137. C8 | #41×C43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#532 | 2 |
| C43×#498 | 2 |
| C43×#493 | 2 |
| C43×#486 | 2 |
| C43×#469 | 2 |
| C43×#442 | 2 |
| C4×M16×C43 | 2 |
| #3184 | 43 |