Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
166 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20295157 | C2 | semidirect |
| 4. #20294776 | C2 | semidirect |
| 6. C8×#11724784 | C2 | semidirect |
| 7. Q8⋊C8×C109 | C2 | semidirect |
| 59. #11724784 | M16 | semidirect |
| 60. #11724784 | SD16 | semidirect |
| 78. C109 | #1590 | semidirect |
| 83. Q8⋊C8 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295157 | 2 |
| C4×#13182016 | 2 |
| #20295103 | 2 |
| #20294776 | 2 |
| #20294755 | 2 |
| C8×#11724784 | 2 |
| Q8⋊C8×C109 | 2 |
| #1590 | 109 |