Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
264 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 74 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⋊#108 | C2 | semidirect |
| 2. C2×#16812768 | C2 | semidirect |
| 4. #20295905 | C2 | semidirect |
| 16. #16812707 | C4 | semidirect |
| 17. #16812706 | C4 | semidirect |
| 19. #16812705 | C4 | semidirect |
| 24. #131×C109 | C4 | semidirect |
| 116. C109 | #1816 | semidirect |
| 128. #131 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D109⋊#108 | 2 |
| C2×#16812768 | 2 |
| #20296017 | 2 |
| #20295905 | 2 |
| #131×D109 | 2 |
| #1816 | 109 |