Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1502 conjugacy classes of subgroups; only the 462 normal subgroups are shown.
This group has 1502 conjugacy classes of subgroups — too many to draw. Only its 462 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C53 | C22⋊C4 |
| commutator | C2×C4 | C23×C4×C53 |
| Frattini, cosocle | C42 | C24×C53 |
| prime radical | C23×D4×C53 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C53 ◁ C22×C42×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#97×C53 | C2 | semidirect |
| 3. C2×C53×#329 | C2 | direct (N × H) |
| 13. C2×#97×C53 | C22 | semidirect |
| 14. C53×#329 | C22 | direct (N × H) |
| 37. #97×C53 | C23 | semidirect |
| 88. C22×#329 | C53 | direct (N × H) |
| 92. C22×C53 | #329 | direct (N × H) |
| 102. C22×#97 | C2×C53 | semidirect |
| 103. C2×#329 | C2×C53 | direct (N × H) |
| 105. C2×C53 | C2×#329 | direct (N × H) |
| 117. C2×#97 | C22×C53 | semidirect |
| 118. #329 | C22×C53 | direct (N × H) |
| 119. C53 | C22×#329 | direct (N × H) |
| 142. #97 | C23×C53 | semidirect |
| 196. C22 | C53×#329 | direct (N × H) |
| 206. C2 | C2×C53×#329 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#124×C53 | 2 |
| C22×#97×C53 | 2 |
| C2×C53×#329 | 2 |
| C22×#329 | 53 |