Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
534 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 1. C2×#16811059 | C2 | semidirect |
| 2. #20284436 | C2 | semidirect |
| 3. C2×#16810890 | C2 | semidirect |
| 4. #20276444 | C2 | semidirect |
| 5. #20276335 | C2 | semidirect |
| 6. #20272826 | C2 | semidirect |
| 7. C2×C53×#361 | C2 | semidirect |
| 206. C2×#361 | D53 | semidirect |
| 240. C53 | #13323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811059 | 2 |
| #20284436 | 2 |
| C2×#16810890 | 2 |
| #20276444 | 2 |
| #20276335 | 2 |
| #20272826 | 2 |
| C2×C53×#361 | 2 |
| #13323 | 53 |