Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
752 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 264 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×C17 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C17 |
| prime radical | C2×C17×#127 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C17×C4⋊Q8 | C2 | semidirect |
| 3. C2×C17×#124 | C2 | semidirect |
| 4. C17×#390 | C2 | semidirect |
| 5. C43×C17 | C2 | semidirect |
| 32. C42×C17 | D4 | semidirect |
| 48. #2858 | C17 | direct (N × H) |
| 57. C4×C17 | #124 | semidirect |
| 59. C2×C4⋊Q8 | C2×C17 | semidirect |
| 61. C2×#124 | C2×C17 | semidirect |
| 62. #390 | C2×C17 | semidirect |
| 63. C43 | C2×C17 | semidirect |
| 79. C17 | #2858 | direct (N × H) |
| 95. C42 | D4×C17 | semidirect |
| 119. C4 | C17×#124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C17×C4⋊Q8 | 2 |
| C2×C17×#127 | 2 |
| C2×C17×#124 | 2 |
| C17×#390 | 2 |
| C43×C17 | 2 |
| #2858 | 17 |