Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
200 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C53 | #2206 |
| commutator, Frattini, cosocle | C2×C16 | C23×C53 |
| prime radical | C53×#2263 | C2 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C53 ◁ C2×C4×C53 ◁ C4×C8×C53 ◁ C4×C16×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C53×#2264 | C2 | semidirect |
| 3. C53×#2249 | C2 | semidirect |
| 4. C53×#2178 | C2 | semidirect |
| 5. C53×#1422 | C2 | semidirect |
| 6. C53×#1420 | C2 | semidirect |
| 7. C53×#1419 | C2 | semidirect |
| 83. #13691 | C53 | direct (N × H) |
| 93. #2264 | C2×C53 | semidirect |
| 95. #2249 | C2×C53 | semidirect |
| 96. #2178 | C2×C53 | semidirect |
| 97. #1422 | C2×C53 | semidirect |
| 98. #1420 | C2×C53 | semidirect |
| 99. #1419 | C2×C53 | semidirect |
| 119. C53 | #13691 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#2264 | 2 |
| C53×#2263 | 2 |
| C53×#2249 | 2 |
| C53×#2178 | 2 |
| C53×#1422 | 2 |
| C53×#1420 | 2 |
| C53×#1419 | 2 |
| #13691 | 53 |