Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
252 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 252 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. D4×#11719908 | C2 | semidirect |
| 2. #20276534 | C2 | semidirect |
| 4. #20272778 | C2 | semidirect |
| 5. #20272671 | C2 | semidirect |
| 6. #20272634 | C2 | semidirect |
| 7. C53×D4⋊C16 | C2 | semidirect |
| 57. #11719922 | C16 | semidirect |
| 74. D4×C53 | C2×C16 | semidirect |
| 83. D212 | C2×C16 | semidirect |
| 93. #88322 | C2×C16 | semidirect |
| 114. D4⋊C16 | D53 | semidirect |
| 136. C53 | #12062 | semidirect |
| 190. D4 | C16×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#11719908 | 2 |
| #20276534 | 2 |
| C8×#11719922 | 2 |
| #20272778 | 2 |
| #20272671 | 2 |
| #20272634 | 2 |
| C53×D4⋊C16 | 2 |
| #12062 | 53 |