Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
426 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×Q8×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#550 | C2 | semidirect |
| 2. D4×Q8×C13 | C2 | semidirect |
| 3. C13×#486 | C2 | semidirect |
| 4. C13×#474 | C2 | semidirect |
| 5. C13×#459 | C2 | semidirect |
| 6. C8×Q8×C13 | C2 | semidirect |
| 7. C4×C13×D8 | C2 | semidirect |
| 44. #3358 | C13 | direct (N × H) |
| 48. Q8×C13 | D8 | semidirect |
| 54. D4×C13 | #41 | semidirect |
| 64. #550 | C2×C13 | semidirect |
| 65. D4×Q8 | C2×C13 | semidirect |
| 66. #486 | C2×C13 | semidirect |
| 67. #474 | C2×C13 | semidirect |
| 68. #459 | C2×C13 | semidirect |
| 69. C8×Q8 | C2×C13 | semidirect |
| 70. C4×D8 | C2×C13 | semidirect |
| 125. C13 | #3358 | direct (N × H) |
| 129. Q8 | C13×D8 | semidirect |
| 135. D4 | C13×#41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#550 | 2 |
| D4×Q8×C13 | 2 |
| C13×#486 | 2 |
| C13×#474 | 2 |
| C13×#459 | 2 |
| C8×Q8×C13 | 2 |
| C4×C13×D8 | 2 |
| #3358 | 13 |