Finite Group DatabasebetaFinite Group DatabasebetaOrder 6592.
158 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D103 |
| commutator, socle | C22×C103 | C22×C4 |
| Fitting | C22⋊C8×C103 | C2 |
| hypercenter | C22⋊C8 | D103 |
| hypocenter | C103 | #408 |
| LCS | G ▷ C22×C103 ▷ C103 | |
| UCS | C1 ◁ C2×C4 ◁ C22⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13110088 | C2 | semidirect |
| 3. C2×C8×D103 | C2 | semidirect |
| 4. C22⋊(C103⋊C8) | C2 | semidirect |
| 5. (C2×D103)⋊C8 | C2 | semidirect |
| 6. (C2×D103)⋊C8 | C2 | semidirect |
| 7. C22⋊C8×C103 | C2 | semidirect |
| 65. C103 | #408 | semidirect |
| 73. C22⋊C8 | D103 | semidirect |