Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
266 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | D4×D97 |
| commutator | C4×C97 | C24 |
| Frattini | C4 | C23×D97 |
| Fitting | C2×SD16×C97 | C2 |
| socle | C22×C97 | C2×D4 |
| hypercenter | C2×SD16 | D97 |
| hypocenter | C97 | C2×#135 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×SD16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13095512 | C2 | semidirect |
| 2. C2×#13095510 | C2 | semidirect |
| 3. #15690831 | C2 | direct (N × H) |
| 4. C2×#13095501 | C2 | semidirect |
| 5. C2×#13095500 | C2 | semidirect |
| 6. C2×#13095496 | C2 | semidirect |
| 7. C2×C8×D97 | C2 | semidirect |
| 8. C2×SD16×C97 | C2 | semidirect |
| 10. #13095512 | C22 | semidirect |
| 12. #13095510 | C22 | semidirect |
| 20. #13095501 | C22 | semidirect |
| 21. #13095500 | C22 | semidirect |
| 22. #13095496 | C22 | semidirect |
| 24. C8×D97 | C22 | semidirect |
| 27. SD16×C97 | C22 | semidirect |
| 65. C2×C97 | #135 | semidirect |
| 69. C97 | C2×#135 | semidirect |
| 76. C2×SD16 | D97 | semidirect |
| 94. SD16 | C2×D97 | semidirect |
| 137. C2 | #15690831 | direct (N × H) |