Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
368 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 202 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. #20296085 | C2 | direct (N × H) |
| 2. C2×#16812774 | C2 | semidirect |
| 3. C2×#16812773 | C2 | semidirect |
| 4. C2×D109⋊C16 | C2 | semidirect |
| 5. C22×#13182032 | C2 | semidirect |
| 7. #16812774 | C22 | semidirect |
| 8. #16812773 | C22 | semidirect |
| 9. D109⋊C16 | C22 | semidirect |
| 13. C2×#13182032 | C22 | semidirect |
| 66. C2×C109 | #504 | semidirect |
| 70. C109 | C2×#504 | semidirect |
| 137. C2 | #20296085 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296085 | 2 |
| C2×#16812774 | 2 |
| C2×#16812773 | 2 |
| C2×D109⋊C16 | 2 |
| C22×#13182032 | 2 |
| C2×#16812707 | 2 |
| C2×#504 | 109 |