Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
266 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×#87604 |
| commutator | C2×C97 | C23×C4 |
| Frattini | C2 | C23×#87604 |
| Fitting | C2×D4×C97 | C4 |
| socle | C22×C97 | C22×C4 |
| hypercenter | C2×D4 | #87604 |
| hypocenter | C97 | C2×#131 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15690897 | C2 | direct (N × H) |
| 2. C2×#13095521 | C2 | semidirect |
| 3. C2×#13095520 | C2 | semidirect |
| 4. C2×#13095519 | C2 | semidirect |
| 5. C22×#11715897 | C2 | semidirect |
| 7. #13095521 | C22 | semidirect |
| 8. #13095520 | C22 | semidirect |
| 9. #13095519 | C22 | semidirect |
| 13. C2×#11715897 | C22 | semidirect |
| 46. C2×C97 | #131 | semidirect |
| 49. C97 | C2×#131 | semidirect |
| 97. C2 | #15690897 | direct (N × H) |