Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
332 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #13093996 |
| commutator | C2×C4×C47 | C22×C4 |
| Frattini | C22×C4 | C22×D47 |
| Fitting | C47×#575 | C2 |
| socle | C2×C47 | #386 |
| hypercenter | #575 | D47 |
| hypocenter | C47 | #1906 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #575 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #41×Dic47 | C2 | semidirect |
| 2. #15689140 | C2 | semidirect |
| 3. C2×#13093951 | C2 | semidirect |
| 4. #15689097 | C2 | semidirect |
| 5. #15688895 | C2 | semidirect |
| 6. #15688884 | C2 | semidirect |
| 24. #137×C47 | C4 | semidirect |
| 26. AGL(1,ℤ/8)×C47 | C4 | semidirect |
| 37. C2×Q8×C47 | C2×C4 | semidirect |
| 41. C2×D4×C47 | C2×C4 | semidirect |
| 53. M16×C47 | C2×C4 | semidirect |
| 137. C47 | #1906 | semidirect |
| 141. #137 | Dic47 | semidirect |
| 143. AGL(1,ℤ/8) | Dic47 | semidirect |
| 167. C2×Q8 | C2×Dic47 | semidirect |
| 171. C2×D4 | C2×Dic47 | semidirect |
| 185. M16 | C2×Dic47 | semidirect |