Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
500 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 204 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. #20296053 | C2 | semidirect |
| 2. #20296043 | C2 | semidirect |
| 3. D109⋊(C22⋊C8) | C2 | semidirect |
| 4. C2×C22⋊#11724786 | C2 | semidirect |
| 6. C2×D109⋊C8 | C22 | semidirect |
| 7. C22×#11724786 | C22 | semidirect |
| 8. #16812766 | C22 | semidirect |
| 9. #16812756 | C22 | semidirect |
| 11. C22⋊#11724786 | C22 | semidirect |
| 12. C4×#11724786 | C22 | semidirect |
| 26. C2×C22⋊D109 | C8 | semidirect |
| 47. C23×C109 | C2×C8 | semidirect |
| 52. C22×D109 | C2×C8 | semidirect |
| 58. C22⋊D109 | C2×C8 | semidirect |
| 63. C2×Dic109 | C2×C8 | semidirect |
| 96. C109 | #2972 | semidirect |
| 147. C23 | D109⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296053 | 2 |
| #20296043 | 2 |
| D109⋊(C22⋊C8) | 2 |
| C2×C22⋊#11724786 | 2 |
| C2×#16812659 | 2 |
| #2972 | 109 |