Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
402 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 183 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 |
|---|---|---|
| 2. Q8×#11724784 | C2 | semidirect |
| 3. #20295105 | C2 | semidirect |
| 4. #20295103 | C2 | semidirect |
| 5. #20295082 | C2 | semidirect |
| 6. C4×#13182012 | C2 | semidirect |
| 7. C8×Q8×C109 | C2 | semidirect |
| 44. Q8×C109 | M16 | semidirect |
| 57. C8×C109 | #41 | semidirect |
| 59. #11724784 | #41 | semidirect |
| 76. C109 | #2971 | semidirect |
| 79. C8×Q8 | D109 | semidirect |
| 120. Q8 | #13182012 | semidirect |
| 135. C8 | #13182030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13182030 | 2 |
| Q8×#11724784 | 2 |
| #20295105 | 2 |
| #20295103 | 2 |
| #20295082 | 2 |
| C4×#13182012 | 2 |
| C8×Q8×C109 | 2 |
| #2971 | 109 |