Finite Group DatabasebetaFinite Group DatabasebetaOrder 1216.
168 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 168 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 |
|---|---|---|
| 1. #10597435 | C2 | semidirect |
| 2. #10597395 | C2 | semidirect |
| 3. #10597354 | C2 | semidirect |
| 4. #10597320 | C2 | semidirect |
| 5. C19×#104 | C2 | semidirect |
| 6. #10597280 | C2 | semidirect |
| 7. #10597262 | C2 | semidirect |
| 17. C2×D76 | C22 | semidirect |
| 18. M16×C19 | C22 | semidirect |
| 19. C42×C19 | C22 | semidirect |
| 22. #64520 | C22 | semidirect |
| 28. Q8×C19 | D4 | semidirect |
| 30. D4×C19 | D4 | semidirect |
| 42. D76 | D4 | semidirect |
| 45. Dic38 | D4 | semidirect |
| 73. #104 | D19 | semidirect |
| 75. C19 | #453 | semidirect |
| 91. M16 | C2×D19 | semidirect |
| 92. C42 | C2×D19 | semidirect |
| 97. Q8 | D76 | semidirect |
| 108. D4 | D76 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10597435 | 2 |
| #10597395 | 2 |
| #10597354 | 2 |
| #10597320 | 2 |
| C19×#104 | 2 |
| #10597280 | 2 |
| #10597262 | 2 |
| #453 | 19 |