Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
170 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22⋊#87604 |
| commutator | C4×C97 | C22×C4 |
| Frattini | C4 | C22×#87604 |
| Fitting | #41×C97 | C4 |
| socle | C2×C97 | C2×C22⋊C4 |
| hypercenter | #41 | #87604 |
| hypocenter | C97 | C2×#104 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D97⋊M16 | C2 | semidirect |
| 2. C2×C4×#87604 | C2 | semidirect |
| 3. #15690875 | C2 | semidirect |
| 4. #15690874 | C2 | semidirect |
| 7. #13095521 | C22 | semidirect |
| 11. C4×#87604 | C22 | semidirect |
| 14. #13095511 | C4 | semidirect |
| 17. Q8×D97 | C4 | semidirect |
| 19. D4×D97 | C4 | semidirect |
| 22. #41×C97 | C4 | semidirect |
| 27. Q8×C97 | C2×C4 | semidirect |
| 29. D4×C97 | C2×C4 | semidirect |
| 38. D388 | C2×C4 | semidirect |
| 47. Dic194 | C2×C4 | semidirect |
| 68. D97 | #104 | semidirect |
| 69. C97 | C2×#104 | semidirect |
| 81. #41 | #87604 | semidirect |
| 97. Q8 | C2×#87604 | semidirect |
| 104. D4 | C2×#87604 | semidirect |