Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
600 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 258 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. C2×#15690879 | C2 | direct (N × H) |
| 7. #15690879 | C22 | direct (N × H) |
| 9. C22×#11715895 | C4 | semidirect |
| 10. C2×C8×D97 | C4 | semidirect |
| 12. C22×C8×C97 | C4 | semidirect |
| 23. C2×#11715895 | C2×C4 | semidirect |
| 24. C8×D97 | C2×C4 | semidirect |
| 27. C2×C8×C97 | C2×C4 | semidirect |
| 44. C8×C97 | C22×C4 | semidirect |
| 45. #11715895 | C22×C4 | semidirect |
| 46. C22×C97 | #107 | semidirect |
| 48. C2×D97 | #107 | semidirect |
| 58. C2×C97 | C2×#107 | semidirect |
| 60. D97 | C2×#107 | semidirect |
| 64. C97 | C22×#107 | semidirect |
| 73. C22×C8 | #87604 | semidirect |
| 89. C2×C8 | C2×#87604 | semidirect |
| 109. C8 | C22×#87604 | semidirect |
| 115. C22 | #15690879 | direct (N × H) |
| 125. C2 | C2×#15690879 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#87604 | 2 |
| C2×#15690879 | 2 |
| C22×C8×D97 | 2 |
| C22×#107 | 97 |