Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
564 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C47 | C2×C22⋊C4 |
| commutator | C23 | C22×C4×C47 |
| Frattini, cosocle | C22×C4 | C23×C47 |
| prime radical | C24×C47 | C2×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#101×C47 | C2 | semidirect |
| 49. C22×C47 | #101 | semidirect |
| 55. #1784 | C47 | direct (N × H) |
| 61. C2×#101 | C2×C47 | semidirect |
| 63. C47 | #1784 | direct (N × H) |
| 109. C22 | #101×C47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Q8×C47 | 2 |
| C2×#101×C47 | 2 |
| C47×#407 | 2 |
| #1784 | 47 |