Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
728 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C13 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C13×#127 | C2 | semidirect |
| 2. C2×C13×#121 | C2 | semidirect |
| 3. C2×C13×#117 | C2 | semidirect |
| 4. C13×#394 | C2 | semidirect |
| 5. C13×#392 | C2 | semidirect |
| 6. C13×#390 | C2 | semidirect |
| 7. C13×#382 | C2 | semidirect |
| 34. C22×C4×C13 | D4 | semidirect |
| 46. C42×C13 | D4 | semidirect |
| 47. #2619 | C13 | direct (N × H) |
| 74. C2×#127 | C2×C13 | semidirect |
| 75. C2×#121 | C2×C13 | semidirect |
| 76. C2×#117 | C2×C13 | semidirect |
| 77. #394 | C2×C13 | semidirect |
| 78. #392 | C2×C13 | semidirect |
| 79. #390 | C2×C13 | semidirect |
| 80. #382 | C2×C13 | semidirect |
| 131. C22×C4 | D4×C13 | semidirect |
| 143. C42 | D4×C13 | semidirect |
| 144. C13 | #2619 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#127 | 2 |
| C2×C13×#121 | 2 |
| C2×C13×#117 | 2 |
| C13×#394 | 2 |
| C13×#392 | 2 |
| C13×#390 | 2 |
| C13×#382 | 2 |
| #2619 | 13 |