Finite Group DatabasebetaFinite Group DatabasebetaOrder 6592.
292 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D103 |
| commutator, socle | C22×C103 | C24 |
| Fitting | C4⋊Q8×C103 | C2 |
| hypercenter | C4⋊Q8 | D103 |
| hypocenter | C103 | #547 |
| LCS | G ▷ C22×C103 ▷ C103 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13110106 | C2 | semidirect |
| 2. #15693006 | C2 | semidirect |
| 3. #15692997 | C2 | semidirect |
| 4. #15692996 | C2 | semidirect |
| 5. C4×D412 | C2 | semidirect |
| 6. C4×D412 | C2 | semidirect |
| 7. C4⋊C4×D103 | C2 | semidirect |
| 8. C4⋊Q8×C103 | C2 | semidirect |
| 37. D412 | D4 | semidirect |
| 51. C4×C103 | #41 | semidirect |
| 59. C103 | #547 | semidirect |
| 62. C4⋊Q8 | D103 | semidirect |
| 113. C4 | #13110106 | semidirect |