Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
428 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 88 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. D109⋊(C4⋊C8) | C2 | semidirect |
| 2. C2×#16812761 | C2 | semidirect |
| 3. C4×C4⋊#89137 | C2 | semidirect |
| 15. #16812696 | C4 | semidirect |
| 18. #16812695 | C4 | semidirect |
| 20. #127×C109 | C4 | semidirect |
| 25. C4⋊#89137 | D4 | semidirect |
| 96. C4×C109 | #102 | semidirect |
| 99. Dic109 | #102 | semidirect |
| 110. C109 | #1982 | semidirect |
| 123. #127 | #89137 | semidirect |
| 210. C4 | #16812761 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D109⋊(C4⋊C8) | 2 |
| C2×#16812761 | 2 |
| C4×C4⋊#89137 | 2 |
| #127×D109 | 2 |
| #1982 | 109 |