Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
572 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×#16812719 | C2 | semidirect |
| 2. #20295576 | C2 | semidirect |
| 3. #20295408 | C2 | semidirect |
| 4. #20295405 | C2 | semidirect |
| 5. #20295402 | C2 | semidirect |
| 6. #20295400 | C2 | semidirect |
| 7. #20295398 | C2 | semidirect |
| 8. C2×C4×#11724784 | C2 | semidirect |
| 9. #532×C109 | C2 | semidirect |
| 42. C2×#11724784 | D4 | semidirect |
| 93. C4×C109 | #135 | semidirect |
| 102. C109 | #3147 | semidirect |
| 105. #532 | D109 | semidirect |
| 196. C4 | #16812719 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812719 | 2 |
| #20295576 | 2 |
| #20295408 | 2 |
| #20295405 | 2 |
| #20295402 | 2 |
| #20295400 | 2 |
| #20295398 | 2 |
| C2×C4×#11724784 | 2 |
| #532×C109 | 2 |
| #3147 | 109 |