Finite Group DatabasebetaFinite Group DatabasebetaOrder 6592.
506 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D103 |
| commutator | C22×C103 | C22×C4 |
| Fitting | C2×C22⋊C4×C103 | C2 |
| socle | C23×C103 | C23 |
| hypercenter | C2×C22⋊C4 | D103 |
| hypocenter | C103 | #379 |
| LCS | G ▷ C22×C103 ▷ C103 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C22⋊Dic103 | C2 | semidirect |
| 3. C2×(C2×D103)⋊C4 | C2 | semidirect |
| 4. C2×C22⋊C4×C103 | C2 | semidirect |
| 8. C23×D103 | C4 | semidirect |
| 10. C22×Dic103 | C22 | semidirect |
| 14. C22×C4×C103 | C22 | semidirect |
| 37. C22×C103 | C22⋊C4 | semidirect |
| 47. C2×D103 | C22⋊C4 | semidirect |
| 56. C103 | #379 | semidirect |
| 61. C2×C22⋊C4 | D103 | semidirect |
| 69. C22×C4 | C2×D103 | semidirect |
| 100. C22 | (C2×D103)⋊C4 | semidirect |