Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
552 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20287849 | C2 | semidirect |
| 2. #20285158 | C2 | semidirect |
| 3. #20276444 | C2 | semidirect |
| 4. #20276443 | C2 | semidirect |
| 5. #20275609 | C2 | semidirect |
| 6. #20272794 | C2 | semidirect |
| 7. C53×#3414 | C2 | semidirect |
| 64. C2×#11719908 | D4 | semidirect |
| 82. C2×Q16×C53 | D4 | semidirect |
| 86. C2×D8×C53 | D4 | semidirect |
| 94. C2×C16×C53 | D4 | semidirect |
| 229. #3414 | D53 | semidirect |
| 269. C53 | #13340 | semidirect |
| 290. C2×Q16 | C22⋊D53 | semidirect |
| 299. C2×D8 | C22⋊D53 | semidirect |
| 323. C2×C16 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287849 | 2 |
| #20285158 | 2 |
| #20276444 | 2 |
| #20276443 | 2 |
| #20275609 | 2 |
| #20272794 | 2 |
| C53×#3414 | 2 |
| #13340 | 53 |