Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
494 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #364×D53 | C2 | semidirect |
| 3. #20272752 | C2 | semidirect |
| 4. #20272751 | C2 | semidirect |
| 5. C53×#1357 | C2 | semidirect |
| 13. #16810444 | C22 | semidirect |
| 16. C53×#364 | C22 | semidirect |
| 110. #1357 | D53 | direct (N × H) |
| 116. D53 | #1357 | direct (N × H) |
| 127. #364 | C2×D53 | semidirect |
| 128. C53 | C2×#1357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #493×D53 | 2 |
| #364×D53 | 2 |
| #20272752 | 2 |
| #20272751 | 2 |
| C53×#1357 | 2 |
| C2×#1357 | 53 |