Finite Group DatabasebetaFinite Group DatabasebetaOrder 14912.
152 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 39 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. #21418566 | C2 | semidirect |
| 3. #21418524 | C2 | semidirect |
| 4. #21418462 | C2 | semidirect |
| 5. #21418461 | C2 | semidirect |
| 6. #21418451 | C2 | semidirect |
| 7. #137×C233 | C2 | semidirect |
| 17. #16836578 | C22 | semidirect |
| 19. C4×Dic233 | C22 | semidirect |
| 21. C2×Q8×C233 | C22 | semidirect |
| 24. M16×C233 | C22 | semidirect |
| 64. C233 | #455 | semidirect |
| 68. #137 | D233 | semidirect |
| 77. C2×Q8 | C2×D233 | semidirect |
| 87. M16 | C2×D233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21418581 | 2 |
| #21418566 | 2 |
| #21418524 | 2 |
| #21418462 | 2 |
| #21418461 | 2 |
| #21418451 | 2 |
| #137×C233 | 2 |
| #455 | 233 |