Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
500 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 170 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. C2×#16812787 | C2 | semidirect |
| 2. #20296060 | C2 | semidirect |
| 3. #20296054 | C2 | semidirect |
| 4. #20296030 | C2 | semidirect |
| 5. #20296001 | C2 | semidirect |
| 6. C4×D109⋊C8 | C2 | semidirect |
| 29. D109⋊C8 | D4 | semidirect |
| 75. C4×C109 | #131 | semidirect |
| 84. C109 | #2931 | semidirect |
| 162. C4 | #16812787 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812787 | 2 |
| #20296060 | 2 |
| #20296054 | 2 |
| #20296030 | 2 |
| #20296001 | 2 |
| C4×D109⋊C8 | 2 |
| #20295577 | 2 |
| #2931 | 109 |