Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
252 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 86 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. #20291094 | C2 | semidirect |
| 2. D4×#11719910 | C2 | semidirect |
| 3. #20289738 | C2 | semidirect |
| 4. #20289666 | C2 | semidirect |
| 5. D4⋊#11719910 | C2 | semidirect |
| 6. #20289630 | C2 | semidirect |
| 54. #11719922 | C16 | semidirect |
| 74. D4×C53 | C2×C16 | semidirect |
| 83. D212 | C2×C16 | semidirect |
| 91. #88322 | C2×C16 | semidirect |
| 136. C53 | #12062 | semidirect |
| 190. D4 | D53⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291094 | 2 |
| D4×#11719910 | 2 |
| #20289738 | 2 |
| #20289666 | 2 |
| D4⋊#11719910 | 2 |
| #20289630 | 2 |
| #20273507 | 2 |
| #12062 | 53 |