Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
480 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 2. #20289655 | C2 | semidirect |
| 3. #20289645 | C2 | semidirect |
| 40. #124×C53 | C8 | semidirect |
| 47. C2×Q8×C53 | C2×C8 | semidirect |
| 67. C42×C53 | C2×C8 | semidirect |
| 158. C53 | #11477 | semidirect |
| 164. #124 | #88324 | semidirect |
| 189. C2×Q8 | C2×#88324 | semidirect |
| 221. C42 | C2×#88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289951 | 2 |
| #20289655 | 2 |
| #20289645 | 2 |
| #124×Dic53 | 2 |
| #11477 | 53 |