Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
612 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 170 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×#261 | C2 | semidirect |
| 4. (C2×#261)⋊Q8 | C2 | semidirect |
| 6. #11719071 | C2 | semidirect |
| 7. #11719070 | C2 | semidirect |
| 8. #11719059 | C2 | semidirect |
| 9. #11719057 | C2 | semidirect |
| 24. C13×#124 | C4 | semidirect |
| 25. #88201 | C4 | semidirect |
| 26. #88190 | C4 | semidirect |
| 27. #88139 | C4 | semidirect |
| 29. #88129 | C4 | semidirect |
| 42. C2×Q8×C13 | C2×C4 | semidirect |
| 53. C2×Dic26 | C2×C4 | semidirect |
| 54. C2×Dic26 | C2×C4 | semidirect |
| 64. C13×C22⋊C4 | C2×C4 | semidirect |
| 65. C42×C13 | C2×C4 | semidirect |
| 66. C22⋊Dic13 | C2×C4 | semidirect |
| 67. #6103 | C2×C4 | semidirect |
| 68. #6103 | C2×C4 | semidirect |
| 69. C4×Dic13 | C2×C4 | semidirect |
| 70. C4×Dic13 | C2×C4 | semidirect |
| 148. #124 | #261 | semidirect |
| 177. C2×Q8 | C2×#261 | semidirect |
| 202. C22⋊C4 | C2×#261 | semidirect |
| 208. C42 | C2×#261 | semidirect |
| 209. C13 | #2326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#261 | 2 |
| C2×D4×#261 | 2 |
| D13×#124 | 2 |
| (C2×#261)⋊Q8 | 2 |
| #11719151 | 2 |
| #11719071 | 2 |
| #11719070 | 2 |
| #11719059 | 2 |
| #11719057 | 2 |
| #2326 | 13 |