Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
602 conjugacy classes of subgroups; only the 305 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 305 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. Q8×#11924040 | C2 | semidirect |
| 2. D4×#11924040 | C2 | semidirect |
| 3. #22627128 | C2 | semidirect |
| 4. C2×C4×#11924040 | C2 | semidirect |
| 39. #11924040 | #41 | direct (N × H) |
| 55. #41×C73 | C16 | semidirect |
| 60. Q8×C73 | C2×C16 | semidirect |
| 61. D4×C73 | C2×C16 | semidirect |
| 62. C2×C4×C73 | C2×C16 | semidirect |
| 97. C73 | C16×#41 | semidirect |
| 130. #41 | #11924040 | direct (N × H) |
| 152. Q8 | C2×#11924040 | semidirect |
| 153. D4 | C2×#11924040 | semidirect |
| 161. C2×C4 | C2×#11924040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11924040 | 2 |
| D4×#11924040 | 2 |
| #22627128 | 2 |
| C2×C4×#11924040 | 2 |
| #41×#10596833 | 2 |
| C16×#41 | 73 |