Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
320 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 88 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. #20261671 | C2 | semidirect |
| 5. #20261607 | C2 | semidirect |
| 6. #20261606 | C2 | semidirect |
| 9. Q8×#87604 | C4 | semidirect |
| 11. D4×#87604 | C4 | semidirect |
| 17. #15690875 | C4 | semidirect |
| 18. #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 |
| 43. C4×#87604 | C2×C4 | semidirect |
| 57. #13095495 | C2×C4 | semidirect |
| 61. C4×Dic97 | C2×C4 | semidirect |
| 63. M16×C97 | C2×C4 | semidirect |
| 64. C42×C97 | C2×C4 | semidirect |
| 127. C97 | #1759 | semidirect |
| 152. #104 | #87604 | semidirect |
| 175. M16 | C2×#87604 | semidirect |
| 191. C42 | C2×#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 |
| #20261671 | 2 |
| #20261607 | 2 |
| #20261606 | 2 |
| #104×D97 | 2 |
| #1759 | 97 |