Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
332 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 68 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. D109⋊#131 | C2 | semidirect |
| 2. #20296017 | C2 | semidirect |
| 3. C2×#16812761 | C2 | semidirect |
| 4. D109⋊#100 | C2 | semidirect |
| 5. #20295905 | C2 | semidirect |
| 6. #20295901 | C2 | semidirect |
| 24. #16812727 | C4 | semidirect |
| 26. #16812725 | C4 | semidirect |
| 27. #16812724 | C4 | semidirect |
| 32. AGL(1,ℤ/8)×C109 | C4 | semidirect |
| 157. C109 | #1907 | semidirect |
| 172. AGL(1,ℤ/8) | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D109⋊#131 | 2 |
| #20296017 | 2 |
| C2×#16812761 | 2 |
| D109⋊#100 | 2 |
| #20295905 | 2 |
| #20295901 | 2 |
| AGL(1,ℤ/8)×D109 | 2 |
| #1907 | 109 |