Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
540 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 114 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 | #459 |
| commutator, Frattini, cosocle | C22×C8 | C23×C53 |
| prime radical | C2×C53×#493 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ C2×C4×C8×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C53×#361 | C2 | semidirect |
| 3. C53×#2140 | C2 | semidirect |
| 4. C53×#1945 | C2 | semidirect |
| 5. C53×#1376 | C2 | semidirect |
| 40. #107×C53 | D4 | semidirect |
| 99. #13413 | C53 | direct (N × H) |
| 115. C2×#361 | C2×C53 | semidirect |
| 116. #2140 | C2×C53 | semidirect |
| 117. #1945 | C2×C53 | semidirect |
| 118. #1376 | C2×C53 | semidirect |
| 136. C53 | #13413 | direct (N × H) |
| 159. #107 | D4×C53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C53×#493 | 2 |
| C2×C53×#361 | 2 |
| C53×#2140 | 2 |
| C53×#1945 | 2 |
| C53×#1376 | 2 |
| #13413 | 53 |