Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
532 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 532 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. #20287849 | C2 | semidirect |
| 2. #20284431 | C2 | semidirect |
| 3. #20284378 | C2 | semidirect |
| 4. #20276444 | C2 | semidirect |
| 5. #20276344 | C2 | semidirect |
| 6. #20272813 | C2 | semidirect |
| 7. C2×C53×#360 | C2 | semidirect |
| 66. C2×#11719908 | D4 | semidirect |
| 68. #13133153 | D4 | semidirect |
| 78. C2×Q16×C53 | D4 | semidirect |
| 80. C2×D8×C53 | D4 | semidirect |
| 223. C2×#360 | D53 | semidirect |
| 259. C53 | #13318 | semidirect |
| 277. C2×Q16 | D212 | semidirect |
| 281. C2×D8 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287849 | 2 |
| #20284431 | 2 |
| #20284378 | 2 |
| #20276444 | 2 |
| #20276344 | 2 |
| #20272813 | 2 |
| C2×C53×#360 | 2 |
| #13318 | 53 |