Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
362 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C53 | #95 |
| commutator | C23 | C4×C8×C53 |
| Frattini, cosocle | C22×C42 | C22×C53 |
| prime radical | C24×C53 | C42 |
| LCS | G ▷ C23 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C53 ◁ C22×C42×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 29. C22⋊C8×C53 | C8 | semidirect |
| 98. #7033 | C53 | direct (N × H) |
| 145. C53 | #7033 | direct (N × H) |
| 161. C22⋊C8 | C8×C53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#1817 | 2 |
| C53×#1797 | 2 |
| C53×#1749 | 2 |
| #7033 | 53 |