Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
256 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 73 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. #20295078 | C2 | semidirect |
| 3. C4⋊C8×D109 | C2 | semidirect |
| 4. #20294772 | C2 | semidirect |
| 5. #20294769 | C2 | semidirect |
| 6. #20294769 | C2 | semidirect |
| 7. #332×C109 | C2 | semidirect |
| 98. C109 | #1540 | semidirect |
| 103. #332 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295577 | 2 |
| #20295078 | 2 |
| C4⋊C8×D109 | 2 |
| #20294772 | 2 |
| #20294769 | 2 |
| #332×C109 | 2 |
| #1540 | 109 |