Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
204 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20295402 | C2 | semidirect |
| 2. #20295221 | C2 | semidirect |
| 3. D4×#11724784 | C2 | semidirect |
| 4. #20294778 | C2 | semidirect |
| 5. #20294770 | C2 | semidirect |
| 6. #20294769 | C2 | semidirect |
| 7. #459×C109 | C2 | semidirect |
| 53. D4×C109 | D8 | semidirect |
| 69. #11724784 | D8 | semidirect |
| 93. C109 | #1667 | semidirect |
| 96. #459 | D109 | semidirect |
| 151. D4 | #13182014 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295402 | 2 |
| #20295221 | 2 |
| D4×#11724784 | 2 |
| #20294778 | 2 |
| #20294770 | 2 |
| #20294769 | 2 |
| #459×C109 | 2 |
| #1667 | 109 |