Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
350 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 184 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. #20289630 | C2 | semidirect |
| 3. #20289628 | C2 | semidirect |
| 44. C8×D53 | C16 | semidirect |
| 59. C8×C53 | C2×C16 | semidirect |
| 61. #88322 | C2×C16 | semidirect |
| 81. D53 | #1312 | semidirect |
| 92. C53 | C2×#1312 | semidirect |
| 140. C8 | D53⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D53⋊C16 | 2 |
| #20289630 | 2 |
| #20289628 | 2 |
| C82×D53 | 2 |
| C2×#1312 | 53 |