Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
360 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 3. M16×#87604 | C2 | semidirect |
| 4. C42×#87604 | C2 | semidirect |
| 5. #20261607 | C2 | semidirect |
| 6. #20261606 | C2 | semidirect |
| 9. Q8×#87604 | C4 | semidirect |
| 11. D4×#87604 | C4 | semidirect |
| 18. #15690875 | C4 | semidirect |
| 19. #15690874 | C4 | semidirect |
| 25. #15690738 | C4 | semidirect |
| 26. #15690737 | C4 | semidirect |
| 27. #15690736 | C4 | semidirect |
| 28. #104×C97 | C4 | semidirect |
| 32. #13095521 | C2×C4 | semidirect |
| 44. C4×#87604 | C2×C4 | semidirect |
| 58. #13095495 | C2×C4 | semidirect |
| 62. C4×Dic97 | C2×C4 | semidirect |
| 64. M16×C97 | C2×C4 | semidirect |
| 65. C42×C97 | C2×C4 | semidirect |
| 75. Q8×C97 | C42 | semidirect |
| 77. D4×C97 | C42 | semidirect |
| 88. D388 | C42 | semidirect |
| 98. Dic194 | C42 | semidirect |
| 112. #87604 | #104 | direct (N × H) |
| 128. C97 | C4×#104 | semidirect |
| 154. #104 | #87604 | direct (N × H) |
| 176. M16 | C2×#87604 | semidirect |
| 193. C42 | C2×#87604 | semidirect |
| 198. Q8 | C4×#87604 | semidirect |
| 205. D4 | C4×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×#87604 | 2 |
| D97⋊#104 | 2 |
| M16×#87604 | 2 |
| C42×#87604 | 2 |
| #20261607 | 2 |
| #20261606 | 2 |
| #104×D97 | 2 |
| C4×#104 | 97 |