Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
760 conjugacy classes of subgroups; only the 434 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 434 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. C4×D109⋊C8 | C2 | direct (N × H) |
| 3. C2×C4×#11724786 | C2 | semidirect |
| 5. C2×D109⋊C8 | C4 | direct (N × H) |
| 8. C4×#11724786 | C22 | semidirect |
| 16. D109⋊C8 | C2×C4 | direct (N × H) |
| 17. C2×#11724786 | C2×C4 | semidirect |
| 22. C2×C4×D109 | C8 | semidirect |
| 38. C2×C4×C109 | C2×C8 | semidirect |
| 41. C2×Dic109 | C2×C8 | semidirect |
| 47. C4×D109 | C2×C8 | semidirect |
| 49. #11724786 | C22×C4 | semidirect |
| 53. C2×D109 | C4×C8 | semidirect |
| 57. C4×C109 | C22×C8 | semidirect |
| 59. Dic109 | C22×C8 | semidirect |
| 61. C2×C109 | C2×C4×C8 | semidirect |
| 64. D109 | C2×C4×C8 | semidirect |
| 66. C109 | C22×C4×C8 | semidirect |
| 112. C2×C4 | D109⋊C8 | direct (N × H) |
| 126. C4 | C2×D109⋊C8 | direct (N × H) |
| 128. C2 | C4×D109⋊C8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D109⋊C8 | 2 |
| C4×D109⋊C8 | 2 |
| C2×C4×#11724786 | 2 |
| C2×C42×D109 | 2 |
| C22×C4×C8 | 109 |