Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
470 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 78 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×C53 | #342 |
| commutator | C22×C4 | C42×C53 |
| Frattini, cosocle | C22×#41 | C22×C53 |
| prime radical | C22×#41×C53 | C22 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ C22×#41×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C2×#101×C53 | C4 | semidirect |
| 12. C2×C22⋊C8×C53 | C4 | semidirect |
| 110. #7309 | C53 | direct (N × H) |
| 143. C2×#101 | C4×C53 | semidirect |
| 150. C2×C22⋊C8 | C4×C53 | semidirect |
| 152. C53 | #7309 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#1785 | 2 |
| C53×#1782 | 2 |
| C53×#1780 | 2 |
| #7309 | 53 |