Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
820 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 228 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. C2×Q8×#87604 | C2 | semidirect |
| 2. (C2×#87604)⋊Q8 | C2 | semidirect |
| 13. C22×Dic194 | C4 | semidirect |
| 15. C2×Q8×D97 | C4 | semidirect |
| 16. C2×Q8×D97 | C4 | semidirect |
| 20. C22×Q8×C97 | C4 | semidirect |
| 25. C22⋊#87604 | Q8 | direct (N × H) |
| 58. C2×#87604 | C2×Q8 | semidirect |
| 60. Q8×C97 | C22⋊C4 | semidirect |
| 73. Dic194 | C22⋊C4 | semidirect |
| 76. C22×C97 | C4×Q8 | semidirect |
| 82. C2×D97 | C4×Q8 | semidirect |
| 101. C97 | Q8×C22⋊C4 | semidirect |
| 113. C22×Q8 | #87604 | semidirect |
| 158. Q8 | C22⋊#87604 | direct (N × H) |
| 186. C22 | Q8×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#87604 | 2 |
| (C2×#87604)⋊Q8 | 2 |
| #20261677 | 2 |
| C4×C22⋊#87604 | 2 |
| C22×Q8×D97 | 2 |
| Q8×C22⋊C4 | 97 |