Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
176 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 55 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. #20295374 | C2 | semidirect |
| 3. D4×#11724784 | C2 | semidirect |
| 4. #20294776 | C2 | semidirect |
| 5. #20294775 | C2 | semidirect |
| 6. #20294769 | C2 | semidirect |
| 7. #476×C109 | C2 | semidirect |
| 83. C109 | #1677 | semidirect |
| 85. #476 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295374 | 2 |
| #20295221 | 2 |
| D4×#11724784 | 2 |
| #20294776 | 2 |
| #20294775 | 2 |
| #20294769 | 2 |
| #476×C109 | 2 |
| #1677 | 109 |