Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
476 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 90 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. #20291377 | C2 | semidirect |
| 2. #20291031 | C2 | semidirect |
| 3. C2×#16811538 | C2 | semidirect |
| 4. D53⋊#350 | C2 | semidirect |
| 5. #20289794 | C2 | semidirect |
| 6. #20289774 | C2 | semidirect |
| 256. C53 | #12995 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291377 | 2 |
| #20291031 | 2 |
| C2×#16811538 | 2 |
| D53⋊#350 | 2 |
| #20289794 | 2 |
| #20289774 | 2 |
| #20284437 | 2 |
| #12995 | 53 |