Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
162 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 54 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. #20296076 | C2 | semidirect |
| 3. #20295890 | C2 | semidirect |
| 4. #20295876 | C2 | semidirect |
| 6. #20295867 | C2 | semidirect |
| 60. #11724784 | M16 | semidirect |
| 78. C109 | #1592 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296076 | 2 |
| #20296061 | 2 |
| #20295890 | 2 |
| #20295876 | 2 |
| D4⋊#11724786 | 2 |
| #20295867 | 2 |
| #20295117 | 2 |
| #1592 | 109 |