Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
180 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 3. #20295890 | C2 | semidirect |
| 4. #20295889 | C2 | semidirect |
| 5. #20295888 | C2 | semidirect |
| 6. #20295887 | C2 | semidirect |
| 32. #13182012 | C8 | semidirect |
| 58. C8×C109 | C2×C8 | semidirect |
| 60. #11724784 | C2×C8 | semidirect |
| 78. C109 | #1565 | semidirect |
| 138. C8 | D109⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296045 | 2 |
| D109⋊(C4⋊C8) | 2 |
| #20295890 | 2 |
| #20295889 | 2 |
| #20295888 | 2 |
| #20295887 | 2 |
| #20294978 | 2 |
| #1565 | 109 |