Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
462 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 462 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 | C22×D4×C43 | C22 |
| 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. C43×#401 | C2 | semidirect |
| 2. C43×#400 | C2 | semidirect |
| 3. C43×#397 | C2 | semidirect |
| 4. C43×#396 | C2 | semidirect |
| 6. C43×#385 | C2 | semidirect |
| 7. C2×#95×C43 | C2 | semidirect |
| 73. #2643 | C43 | direct (N × H) |
| 79. #401 | C2×C43 | semidirect |
| 80. #400 | C2×C43 | semidirect |
| 81. #397 | C2×C43 | semidirect |
| 82. #396 | C2×C43 | semidirect |
| 84. #385 | C2×C43 | semidirect |
| 85. C2×#95 | C2×C43 | semidirect |
| 86. C43 | #2643 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#401 | 2 |
| C43×#400 | 2 |
| C43×#397 | 2 |
| C43×#396 | 2 |
| C43×#386 | 2 |
| C43×#385 | 2 |
| C2×#95×C43 | 2 |
| #2643 | 43 |