Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
496 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 93 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. C22×D872 | C2 | semidirect |
| 2. C2×#16812673 | C2 | semidirect |
| 3. C2×#16812621 | C2 | semidirect |
| 4. #20294789 | C2 | semidirect |
| 5. C2×C22⋊C8×C109 | C2 | semidirect |
| 25. C2×D436 | D4 | semidirect |
| 32. C4⋊Dic109 | D4 | semidirect |
| 44. C2×C8×C109 | D4 | semidirect |
| 49. C23×C109 | D8 | semidirect |
| 107. C109 | #1999 | semidirect |
| 111. C2×C22⋊C8 | D109 | semidirect |
| 148. C2×C8 | C22⋊D109 | semidirect |
| 163. C23 | D872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D872 | 2 |
| C2×#16812673 | 2 |
| C2×#16812621 | 2 |
| #20294789 | 2 |
| C2×C22⋊C8×C109 | 2 |
| #1999 | 109 |