Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
242 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20276548 | C2 | semidirect |
| 3. #20272784 | C2 | semidirect |
| 4. D4⋊#11719908 | C2 | semidirect |
| 5. #20272669 | C2 | semidirect |
| 6. C16×#88322 | C2 | semidirect |
| 7. C53×#2169 | C2 | semidirect |
| 68. C16×C53 | D8 | semidirect |
| 93. #88322 | M32 | semidirect |
| 110. #2169 | D53 | semidirect |
| 136. C53 | #12039 | semidirect |
| 184. C16 | #11719922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276548 | 2 |
| C8×#11719922 | 2 |
| #20272784 | 2 |
| D4⋊#11719908 | 2 |
| #20272669 | 2 |
| C16×#88322 | 2 |
| C53×#2169 | 2 |
| #12039 | 53 |