Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
526 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 142 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 | C2×#99 |
| commutator | C2×C4 | C22×C8×C53 |
| Frattini, cosocle | C2×C4⋊C4 | C23×C53 |
| prime radical | C24×C53 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ C2×#117×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C53×#1319 | C2 | semidirect |
| 18. C22×Q8×C53 | C8 | semidirect |
| 98. #11434 | C53 | direct (N × H) |
| 118. #1319 | C2×C53 | semidirect |
| 135. C53 | #11434 | direct (N × H) |
| 140. C22×Q8 | C8×C53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#2310 | 2 |
| C53×#1458 | 2 |
| C53×#1319 | 2 |
| #11434 | 53 |