Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
286 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 128 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. #20289738 | C2 | semidirect |
| 3. #20289737 | C2 | semidirect |
| 54. C8×D53 | C16 | semidirect |
| 73. C8×C53 | C2×C16 | semidirect |
| 77. #88322 | C2×C16 | semidirect |
| 99. D53 | #1367 | semidirect |
| 110. C53 | C2×#1367 | semidirect |
| 174. C8 | D53⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊(C4⋊C16) | 2 |
| #20289738 | 2 |
| #20289737 | 2 |
| C82×D53 | 2 |
| C2×#1367 | 53 |