Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
602 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 101 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. #20284742 | C2 | semidirect |
| 2. #20280069 | C2 | semidirect |
| 3. #20273275 | C2 | semidirect |
| 4. #20273143 | C2 | semidirect |
| 5. #20273106 | C2 | semidirect |
| 6. #20272575 | C2 | semidirect |
| 99. C2×D4×C53 | SD16 | semidirect |
| 265. C53 | #9998 | semidirect |
| 335. C2×D4 | #11719923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284742 | 2 |
| #20280069 | 2 |
| #20273275 | 2 |
| #20273143 | 2 |
| #20273106 | 2 |
| #20272575 | 2 |
| C53×#3036 | 2 |
| #9998 | 53 |