Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
932 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 932 conjugacy classes of subgroups — too many to draw. Only its 232 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 |
| 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. C22×#41×C17 | C2 | semidirect |
| 2. C2×C17×#121 | C2 | semidirect |
| 3. C17×#393 | C2 | semidirect |
| 4. C17×#392 | C2 | semidirect |
| 5. C17×#380 | C2 | semidirect |
| 27. C22×C4×C17 | D4 | semidirect |
| 53. #2615 | C17 | direct (N × H) |
| 68. C22×#41 | C2×C17 | semidirect |
| 69. C2×#121 | C2×C17 | semidirect |
| 70. #393 | C2×C17 | semidirect |
| 71. #392 | C2×C17 | semidirect |
| 72. #380 | C2×C17 | semidirect |
| 89. C17 | #2615 | direct (N × H) |
| 100. C22×C4 | D4×C17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#41×C17 | 2 |
| C2×C17×#121 | 2 |
| C17×#393 | 2 |
| C17×#392 | 2 |
| C17×#380 | 2 |
| #2615 | 17 |