Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
278 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 74 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 | #2184 |
| commutator, Frattini, cosocle | C2×C16 | C23×C53 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C53 ◁ C2×C4×C53 ◁ #131×C53 ◁ C53×#504 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C53×#3417 | C2 | semidirect |
| 2. C53×#2263 | C2 | semidirect |
| 3. C2×C53×SD64 | C2 | semidirect |
| 4. C53×#2221 | C2 | semidirect |
| 5. C53×#1420 | C2 | semidirect |
| 6. C53×#1417 | C2 | semidirect |
| 7. C53×#1401 | C2 | semidirect |
| 103. #13670 | C53 | direct (N × H) |
| 114. #3417 | C2×C53 | semidirect |
| 115. #2263 | C2×C53 | semidirect |
| 116. C2×SD64 | C2×C53 | semidirect |
| 117. #2221 | C2×C53 | semidirect |
| 118. #1420 | C2×C53 | semidirect |
| 119. #1417 | C2×C53 | semidirect |
| 120. #1401 | C2×C53 | semidirect |
| 143. C53 | #13670 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#3417 | 2 |
| C53×#2263 | 2 |
| C2×C53×SD64 | 2 |
| C53×#2221 | 2 |
| C53×#1420 | 2 |
| C53×#1417 | 2 |
| C53×#1401 | 2 |
| #13670 | 53 |